Non-Gaussian Merton-Black-Scholes theory /:
This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore ; River Edge, NJ :
World Scientific,
2002.
|
| Schriftenreihe: | Advanced series on statistical science & applied probability ;
v. 9. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory. The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential. |
| Beschreibung: | 1 online resource (xxi, 398 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 385-392) and index. |
| ISBN: | 9789812777485 9812777482 9789810249441 9810249446 |
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| 100 | 1 | |a Boyarchenko, Svetlana I. |1 https://id.oclc.org/worldcat/entity/E39PCjK3FTRyVDm6BygVpkX6JC |0 http://id.loc.gov/authorities/names/no2002074047 | |
| 245 | 1 | 0 | |a Non-Gaussian Merton-Black-Scholes theory / |c Svetlana I. Boyarchenko, Sergei Z. Levendorskiĭ. |
| 260 | |a Singapore ; |a River Edge, NJ : |b World Scientific, |c 2002. | ||
| 300 | |a 1 online resource (xxi, 398 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 380 | |a Statistics | ||
| 490 | 1 | |a Advanced series on statistical science & applied probability ; |v v. 9 | |
| 504 | |a Includes bibliographical references (pages 385-392) and index. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory. The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential. | ||
| 505 | 0 | |a Ch. 1. Introduction. 1.1. The Gaussian Merton-Black-Scholes theory. 1.2. Regular Lévy processes of exponential type. 1.3. Pricing of contingent claims. 1.4. The generalized Black-Scholes equation. 1.5. Analytical methods used in the book. 1.6. An overview of the results covered in the book. 1.7. Commentary -- ch. 2. Lévy processes. 2.1. Basic notation and definitions. 2.2. Lévy processes: general definitions. 2.3. Lévy processes as Markov processes. 2.4. Boundary value problems for the Black-Scholes-type equation. 2.5. Commentary -- ch. 3. Regular Lévy Processes of Exponential type in ID. 3.1. Model classes. 3.2. Two definitions of regular Lévy processes of exponential type. 3.3. Properties of the characteristic exponents and probability densities of RLPE. 3.4. Properties of the infinitesimal generators. 3.5. A "naive approach" to the construction of RLPE or why they are natural from the point of view of the theory of PDO. 3.6. The Wiener-Hopf factorization -- ch. 4. Pricing and hedging of contingent claims of European type. 4.1. Equivalent Martingale measures in a Lévy market. 4.2. Pricing of European options and the generalized Black-Scholes formula. 4.3. Generalized Black-Scholes equation and its properties for different RLPE and different choices of EMM, and implications for parameter fitting. 4.4. Other European options. 4.5. Hedging. 4.6. Commentary -- ch. 5. Perpetual American options. 5.1. The reduction to a free boundary problem for the stationary generalized Black-Scholes equation. 5.2. Perpetual American put: the optimal exercise price and the rational put price. 5.3. Perpetual American call. 5.4. Put-like and call-like options: the case of more general payoffs. 5.5. Commentary -- ch. 6. American options: finite time horizon. 6.1. General discussion. 6.2. Approximations of the American put price. 6.3. American put near expiry -- ch. 7. First-touch digitals. 7.1. An overview. 7.2. Exact pricing formulas for first-touch digitals. 7.3. The Wiener-Hopf factorization with a parameter. 7.4. Price near the barrier. 7.5. Asymptotics as [symbol] -- ch. 8. Barrier options. 8.1. Types of barrier options. 8.2. Down-and-out call option without a rebate. 8.3. Asymptotics of the option price near the barrier. 8.4. Commentary -- ch. 9. Multi-asset contracts. 9.1. Multi-dimensional regular Lévy processes of exponential type. 9.2. European-style contracts. 9.3. Locally risk-minimizing hedging with a portfolio of several assets. 9.4. Weighted discretely sampled geometric average -- ch. 10. Investment under uncertainty and capital accumulation. 10.1. Irreversible investment and uncertainty. 10.2. The investment threshold. 10.3. Capital accumulation under RLPE. 10.4. Computational results. 10.5. Approximate formulas and the comparative statics -- ch. 11. Endogenous default and pricing of the corporate debt. 11.1. An overview. 11.2. Endogenous default. 11.3. Equity of a firm near bankruptcy level and the yield spread for junk bonds. 11.4. The case of a solvent firm. 11.5. Endogenous debt level and endogenous leverage. 11.6. Conclusion. 11.7. Auxiliary results. | |
| 505 | 8 | |a Ch. 12. Fast pricing of European options. 12.1. Introduction. 12.2. Transformation of the pricing formula for the European put. 12.3. FFT and IAC. 12.4. Comparison of FFT and IAC -- ch. 13. Discrete time models. 13.1. Bermudan options and discrete time models. 13.2. A perpetual American put in a discrete time model. 13.3. The Wiener-Hopf factorization. 13.4. Optimal exercise boundary and rational price of the option -- ch. 14. Feller processes of normal inverse Gaussian type. 14.1. Introduction. 14.2. Constructions of NIG-like Feller process via pseudodifferential operators. 14.3. Applications for financial mathematics. 14.4. Discussion and conclusions -- ch. 15. Pseudo-differential operators with constant symbols. 15.1. Introduction. 15.2. Classes of functions. 15.3. Space S'[symbol] of generalized functions on R[symbol]. 15.4. Pseudo-differential operators with constant symbols on R[symbol]. 15.5. The action of PDO in the Sobolev spaces on R[symbol]. 15.6. Parabolic equations. 15.7. The Wiener-Hopf equation on a half-line I. 15.8. Parabolic equations on [0,T] x R[symbol]. 15.9. PDO in the Sobolev spaces with exponential weights, in 1D. 15.10. The Sobolev spaces with exponential weights and PDO on a half-line. 15.11. Parabolic equations in spaces with exponential weights. 15.12. The Wiener-Hopf equation on a half-line II. 15.13. Parabolic equations on R x R[symbol] with exponentially growing data -- ch. 16. Elements of calculus of pseudodifferential operators. 16.1. Basics of the theory of PDO with symbols of the class S[symbol]. 16.2. Operators depending on parameters. 16.3. Operators with symbols holomorphic in a tube domain. 16.4. Proofs of auxiliary technical results. 16.5. Change of variables and pricing of multi-asset contracts. 16.6. Pricing of barrier options under Lévy-like Feller processes. | |
| 650 | 0 | |a Finance |x Mathematical models. |0 http://id.loc.gov/authorities/subjects/sh85048260 | |
| 650 | 6 | |a Finances |x Modèles mathématiques. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x Stochastic Processes. |2 bisacsh | |
| 650 | 7 | |a Finance |x Mathematical models |2 fast | |
| 650 | 7 | |a Processos estocasticos. |2 larpcal | |
| 650 | 7 | |a Processos gaussianos. |2 larpcal | |
| 650 | 7 | |a Finanças (modelos matemáticos) |2 larpcal | |
| 650 | 7 | |a Finance. |2 rasuqam | |
| 650 | 7 | |a Option (Finances) |2 rasuqam | |
| 650 | 7 | |a Modèle mathématique. |2 rasuqam | |
| 700 | 1 | |a Levendorskiĭ, Serge, |d 1951- |1 https://id.oclc.org/worldcat/entity/E39PCjJCFMQcrbwc8PTybG6f4m |0 http://id.loc.gov/authorities/names/n90652806 | |
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| 830 | 0 | |a Advanced series on statistical science & applied probability ; |v v. 9. |0 http://id.loc.gov/authorities/names/n97121977 | |
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| author | Boyarchenko, Svetlana I. |
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| contents | Ch. 1. Introduction. 1.1. The Gaussian Merton-Black-Scholes theory. 1.2. Regular Lévy processes of exponential type. 1.3. Pricing of contingent claims. 1.4. The generalized Black-Scholes equation. 1.5. Analytical methods used in the book. 1.6. An overview of the results covered in the book. 1.7. Commentary -- ch. 2. Lévy processes. 2.1. Basic notation and definitions. 2.2. Lévy processes: general definitions. 2.3. Lévy processes as Markov processes. 2.4. Boundary value problems for the Black-Scholes-type equation. 2.5. Commentary -- ch. 3. Regular Lévy Processes of Exponential type in ID. 3.1. Model classes. 3.2. Two definitions of regular Lévy processes of exponential type. 3.3. Properties of the characteristic exponents and probability densities of RLPE. 3.4. Properties of the infinitesimal generators. 3.5. A "naive approach" to the construction of RLPE or why they are natural from the point of view of the theory of PDO. 3.6. The Wiener-Hopf factorization -- ch. 4. Pricing and hedging of contingent claims of European type. 4.1. Equivalent Martingale measures in a Lévy market. 4.2. Pricing of European options and the generalized Black-Scholes formula. 4.3. Generalized Black-Scholes equation and its properties for different RLPE and different choices of EMM, and implications for parameter fitting. 4.4. Other European options. 4.5. Hedging. 4.6. Commentary -- ch. 5. Perpetual American options. 5.1. The reduction to a free boundary problem for the stationary generalized Black-Scholes equation. 5.2. Perpetual American put: the optimal exercise price and the rational put price. 5.3. Perpetual American call. 5.4. Put-like and call-like options: the case of more general payoffs. 5.5. Commentary -- ch. 6. American options: finite time horizon. 6.1. General discussion. 6.2. Approximations of the American put price. 6.3. American put near expiry -- ch. 7. First-touch digitals. 7.1. An overview. 7.2. Exact pricing formulas for first-touch digitals. 7.3. The Wiener-Hopf factorization with a parameter. 7.4. Price near the barrier. 7.5. Asymptotics as [symbol] -- ch. 8. Barrier options. 8.1. Types of barrier options. 8.2. Down-and-out call option without a rebate. 8.3. Asymptotics of the option price near the barrier. 8.4. Commentary -- ch. 9. Multi-asset contracts. 9.1. Multi-dimensional regular Lévy processes of exponential type. 9.2. European-style contracts. 9.3. Locally risk-minimizing hedging with a portfolio of several assets. 9.4. Weighted discretely sampled geometric average -- ch. 10. Investment under uncertainty and capital accumulation. 10.1. Irreversible investment and uncertainty. 10.2. The investment threshold. 10.3. Capital accumulation under RLPE. 10.4. Computational results. 10.5. Approximate formulas and the comparative statics -- ch. 11. Endogenous default and pricing of the corporate debt. 11.1. An overview. 11.2. Endogenous default. 11.3. Equity of a firm near bankruptcy level and the yield spread for junk bonds. 11.4. The case of a solvent firm. 11.5. Endogenous debt level and endogenous leverage. 11.6. Conclusion. 11.7. Auxiliary results. Ch. 12. Fast pricing of European options. 12.1. Introduction. 12.2. Transformation of the pricing formula for the European put. 12.3. FFT and IAC. 12.4. Comparison of FFT and IAC -- ch. 13. Discrete time models. 13.1. Bermudan options and discrete time models. 13.2. A perpetual American put in a discrete time model. 13.3. The Wiener-Hopf factorization. 13.4. Optimal exercise boundary and rational price of the option -- ch. 14. Feller processes of normal inverse Gaussian type. 14.1. Introduction. 14.2. Constructions of NIG-like Feller process via pseudodifferential operators. 14.3. Applications for financial mathematics. 14.4. Discussion and conclusions -- ch. 15. Pseudo-differential operators with constant symbols. 15.1. Introduction. 15.2. Classes of functions. 15.3. Space S'[symbol] of generalized functions on R[symbol]. 15.4. Pseudo-differential operators with constant symbols on R[symbol]. 15.5. The action of PDO in the Sobolev spaces on R[symbol]. 15.6. Parabolic equations. 15.7. The Wiener-Hopf equation on a half-line I. 15.8. Parabolic equations on [0,T] x R[symbol]. 15.9. PDO in the Sobolev spaces with exponential weights, in 1D. 15.10. The Sobolev spaces with exponential weights and PDO on a half-line. 15.11. Parabolic equations in spaces with exponential weights. 15.12. The Wiener-Hopf equation on a half-line II. 15.13. Parabolic equations on R x R[symbol] with exponentially growing data -- ch. 16. Elements of calculus of pseudodifferential operators. 16.1. Basics of the theory of PDO with symbols of the class S[symbol]. 16.2. Operators depending on parameters. 16.3. Operators with symbols holomorphic in a tube domain. 16.4. Proofs of auxiliary technical results. 16.5. Change of variables and pricing of multi-asset contracts. 16.6. Pricing of barrier options under Lévy-like Feller processes. |
| ctrlnum | (OCoLC)285162851 |
| dewey-full | 519.2/3 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2/3 |
| dewey-search | 519.2/3 |
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| discipline | Mathematik |
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Boyarchenko, Sergei Z. Levendorskiĭ.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Singapore ;</subfield><subfield code="a">River Edge, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">2002.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xxi, 398 pages) :</subfield><subfield code="b">illustrations</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="380" ind1=" " ind2=" "><subfield code="a">Statistics</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Advanced series on statistical science & applied probability ;</subfield><subfield code="v">v. 9</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 385-392) and index.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory. The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Ch. 1. Introduction. 1.1. The Gaussian Merton-Black-Scholes theory. 1.2. Regular Lévy processes of exponential type. 1.3. Pricing of contingent claims. 1.4. The generalized Black-Scholes equation. 1.5. Analytical methods used in the book. 1.6. An overview of the results covered in the book. 1.7. Commentary -- ch. 2. Lévy processes. 2.1. Basic notation and definitions. 2.2. Lévy processes: general definitions. 2.3. Lévy processes as Markov processes. 2.4. Boundary value problems for the Black-Scholes-type equation. 2.5. Commentary -- ch. 3. Regular Lévy Processes of Exponential type in ID. 3.1. Model classes. 3.2. Two definitions of regular Lévy processes of exponential type. 3.3. Properties of the characteristic exponents and probability densities of RLPE. 3.4. Properties of the infinitesimal generators. 3.5. A "naive approach" to the construction of RLPE or why they are natural from the point of view of the theory of PDO. 3.6. The Wiener-Hopf factorization -- ch. 4. Pricing and hedging of contingent claims of European type. 4.1. Equivalent Martingale measures in a Lévy market. 4.2. Pricing of European options and the generalized Black-Scholes formula. 4.3. Generalized Black-Scholes equation and its properties for different RLPE and different choices of EMM, and implications for parameter fitting. 4.4. Other European options. 4.5. Hedging. 4.6. Commentary -- ch. 5. Perpetual American options. 5.1. The reduction to a free boundary problem for the stationary generalized Black-Scholes equation. 5.2. Perpetual American put: the optimal exercise price and the rational put price. 5.3. Perpetual American call. 5.4. Put-like and call-like options: the case of more general payoffs. 5.5. Commentary -- ch. 6. American options: finite time horizon. 6.1. General discussion. 6.2. Approximations of the American put price. 6.3. American put near expiry -- ch. 7. First-touch digitals. 7.1. An overview. 7.2. Exact pricing formulas for first-touch digitals. 7.3. The Wiener-Hopf factorization with a parameter. 7.4. Price near the barrier. 7.5. Asymptotics as [symbol] -- ch. 8. Barrier options. 8.1. Types of barrier options. 8.2. Down-and-out call option without a rebate. 8.3. Asymptotics of the option price near the barrier. 8.4. Commentary -- ch. 9. Multi-asset contracts. 9.1. Multi-dimensional regular Lévy processes of exponential type. 9.2. European-style contracts. 9.3. Locally risk-minimizing hedging with a portfolio of several assets. 9.4. Weighted discretely sampled geometric average -- ch. 10. Investment under uncertainty and capital accumulation. 10.1. Irreversible investment and uncertainty. 10.2. The investment threshold. 10.3. Capital accumulation under RLPE. 10.4. Computational results. 10.5. Approximate formulas and the comparative statics -- ch. 11. Endogenous default and pricing of the corporate debt. 11.1. An overview. 11.2. Endogenous default. 11.3. Equity of a firm near bankruptcy level and the yield spread for junk bonds. 11.4. The case of a solvent firm. 11.5. Endogenous debt level and endogenous leverage. 11.6. Conclusion. 11.7. Auxiliary results.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">Ch. 12. Fast pricing of European options. 12.1. Introduction. 12.2. Transformation of the pricing formula for the European put. 12.3. FFT and IAC. 12.4. Comparison of FFT and IAC -- ch. 13. Discrete time models. 13.1. Bermudan options and discrete time models. 13.2. A perpetual American put in a discrete time model. 13.3. The Wiener-Hopf factorization. 13.4. Optimal exercise boundary and rational price of the option -- ch. 14. Feller processes of normal inverse Gaussian type. 14.1. Introduction. 14.2. Constructions of NIG-like Feller process via pseudodifferential operators. 14.3. Applications for financial mathematics. 14.4. Discussion and conclusions -- ch. 15. Pseudo-differential operators with constant symbols. 15.1. Introduction. 15.2. Classes of functions. 15.3. Space S'[symbol] of generalized functions on R[symbol]. 15.4. Pseudo-differential operators with constant symbols on R[symbol]. 15.5. The action of PDO in the Sobolev spaces on R[symbol]. 15.6. Parabolic equations. 15.7. The Wiener-Hopf equation on a half-line I. 15.8. Parabolic equations on [0,T] x R[symbol]. 15.9. PDO in the Sobolev spaces with exponential weights, in 1D. 15.10. The Sobolev spaces with exponential weights and PDO on a half-line. 15.11. Parabolic equations in spaces with exponential weights. 15.12. The Wiener-Hopf equation on a half-line II. 15.13. Parabolic equations on R x R[symbol] with exponentially growing data -- ch. 16. Elements of calculus of pseudodifferential operators. 16.1. Basics of the theory of PDO with symbols of the class S[symbol]. 16.2. Operators depending on parameters. 16.3. Operators with symbols holomorphic in a tube domain. 16.4. Proofs of auxiliary technical results. 16.5. Change of variables and pricing of multi-asset contracts. 16.6. Pricing of barrier options under Lévy-like Feller processes.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Finance</subfield><subfield code="x">Mathematical models.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85048260</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Finances</subfield><subfield code="x">Modèles mathématiques.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Probability & Statistics</subfield><subfield code="x">Stochastic Processes.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Finance</subfield><subfield code="x">Mathematical models</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Processos estocasticos.</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Processos gaussianos.</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Finanças (modelos matemáticos)</subfield><subfield code="2">larpcal</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Finance.</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Option (Finances)</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Modèle mathématique.</subfield><subfield code="2">rasuqam</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Levendorskiĭ, Serge,</subfield><subfield code="d">1951-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCjJCFMQcrbwc8PTybG6f4m</subfield><subfield code="0">http://id.loc.gov/authorities/names/n90652806</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Boyarchenko, Svetlana I.</subfield><subfield code="t">Non-Gaussian Merton-Black-Scholes theory.</subfield><subfield code="d">Singapore ; River Edge, NJ : World Scientific, 2002</subfield><subfield code="z">9810249446</subfield><subfield code="z">9789810249441</subfield><subfield code="w">(DLC) 2002510652</subfield><subfield code="w">(OCoLC)50323695</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Advanced series on statistical science & applied probability ;</subfield><subfield code="v">v. 9.</subfield><subfield code="0">http://id.loc.gov/authorities/names/n97121977</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210771</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="936" ind1=" " ind2=" "><subfield code="a">BATCHLOAD</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24684733</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL1679307</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">210771</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Internet Archive</subfield><subfield code="b">INAR</subfield><subfield code="n">nongaussianmerto0009boya</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2736152</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn285162851 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:16:35Z |
| institution | BVB |
| isbn | 9789812777485 9812777482 9789810249441 9810249446 |
| language | English |
| oclc_num | 285162851 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xxi, 398 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2002 |
| publishDateSearch | 2002 |
| publishDateSort | 2002 |
| publisher | World Scientific, |
| record_format | marc |
| series | Advanced series on statistical science & applied probability ; |
| series2 | Advanced series on statistical science & applied probability ; |
| spelling | Boyarchenko, Svetlana I. https://id.oclc.org/worldcat/entity/E39PCjK3FTRyVDm6BygVpkX6JC http://id.loc.gov/authorities/names/no2002074047 Non-Gaussian Merton-Black-Scholes theory / Svetlana I. Boyarchenko, Sergei Z. Levendorskiĭ. Singapore ; River Edge, NJ : World Scientific, 2002. 1 online resource (xxi, 398 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier Statistics Advanced series on statistical science & applied probability ; v. 9 Includes bibliographical references (pages 385-392) and index. Print version record. This book introduces an analytically tractable and computationally effective class of non-Gaussian models for shocks (regular Lévy processes of the exponential type) and related analytical methods similar to the initial Merton-Black-Scholes approach, which the authors call the Merton-Black-Scholes theory. The authors have chosen applications interesting for financial engineers and specialists in financial economics, real options, and partial differential equations (especially pseudodifferential operators); specialists in stochastic processes will benefit from the use of the pseudodifferential. Ch. 1. Introduction. 1.1. The Gaussian Merton-Black-Scholes theory. 1.2. Regular Lévy processes of exponential type. 1.3. Pricing of contingent claims. 1.4. The generalized Black-Scholes equation. 1.5. Analytical methods used in the book. 1.6. An overview of the results covered in the book. 1.7. Commentary -- ch. 2. Lévy processes. 2.1. Basic notation and definitions. 2.2. Lévy processes: general definitions. 2.3. Lévy processes as Markov processes. 2.4. Boundary value problems for the Black-Scholes-type equation. 2.5. Commentary -- ch. 3. Regular Lévy Processes of Exponential type in ID. 3.1. Model classes. 3.2. Two definitions of regular Lévy processes of exponential type. 3.3. Properties of the characteristic exponents and probability densities of RLPE. 3.4. Properties of the infinitesimal generators. 3.5. A "naive approach" to the construction of RLPE or why they are natural from the point of view of the theory of PDO. 3.6. The Wiener-Hopf factorization -- ch. 4. Pricing and hedging of contingent claims of European type. 4.1. Equivalent Martingale measures in a Lévy market. 4.2. Pricing of European options and the generalized Black-Scholes formula. 4.3. Generalized Black-Scholes equation and its properties for different RLPE and different choices of EMM, and implications for parameter fitting. 4.4. Other European options. 4.5. Hedging. 4.6. Commentary -- ch. 5. Perpetual American options. 5.1. The reduction to a free boundary problem for the stationary generalized Black-Scholes equation. 5.2. Perpetual American put: the optimal exercise price and the rational put price. 5.3. Perpetual American call. 5.4. Put-like and call-like options: the case of more general payoffs. 5.5. Commentary -- ch. 6. American options: finite time horizon. 6.1. General discussion. 6.2. Approximations of the American put price. 6.3. American put near expiry -- ch. 7. First-touch digitals. 7.1. An overview. 7.2. Exact pricing formulas for first-touch digitals. 7.3. The Wiener-Hopf factorization with a parameter. 7.4. Price near the barrier. 7.5. Asymptotics as [symbol] -- ch. 8. Barrier options. 8.1. Types of barrier options. 8.2. Down-and-out call option without a rebate. 8.3. Asymptotics of the option price near the barrier. 8.4. Commentary -- ch. 9. Multi-asset contracts. 9.1. Multi-dimensional regular Lévy processes of exponential type. 9.2. European-style contracts. 9.3. Locally risk-minimizing hedging with a portfolio of several assets. 9.4. Weighted discretely sampled geometric average -- ch. 10. Investment under uncertainty and capital accumulation. 10.1. Irreversible investment and uncertainty. 10.2. The investment threshold. 10.3. Capital accumulation under RLPE. 10.4. Computational results. 10.5. Approximate formulas and the comparative statics -- ch. 11. Endogenous default and pricing of the corporate debt. 11.1. An overview. 11.2. Endogenous default. 11.3. Equity of a firm near bankruptcy level and the yield spread for junk bonds. 11.4. The case of a solvent firm. 11.5. Endogenous debt level and endogenous leverage. 11.6. Conclusion. 11.7. Auxiliary results. Ch. 12. Fast pricing of European options. 12.1. Introduction. 12.2. Transformation of the pricing formula for the European put. 12.3. FFT and IAC. 12.4. Comparison of FFT and IAC -- ch. 13. Discrete time models. 13.1. Bermudan options and discrete time models. 13.2. A perpetual American put in a discrete time model. 13.3. The Wiener-Hopf factorization. 13.4. Optimal exercise boundary and rational price of the option -- ch. 14. Feller processes of normal inverse Gaussian type. 14.1. Introduction. 14.2. Constructions of NIG-like Feller process via pseudodifferential operators. 14.3. Applications for financial mathematics. 14.4. Discussion and conclusions -- ch. 15. Pseudo-differential operators with constant symbols. 15.1. Introduction. 15.2. Classes of functions. 15.3. Space S'[symbol] of generalized functions on R[symbol]. 15.4. Pseudo-differential operators with constant symbols on R[symbol]. 15.5. The action of PDO in the Sobolev spaces on R[symbol]. 15.6. Parabolic equations. 15.7. The Wiener-Hopf equation on a half-line I. 15.8. Parabolic equations on [0,T] x R[symbol]. 15.9. PDO in the Sobolev spaces with exponential weights, in 1D. 15.10. The Sobolev spaces with exponential weights and PDO on a half-line. 15.11. Parabolic equations in spaces with exponential weights. 15.12. The Wiener-Hopf equation on a half-line II. 15.13. Parabolic equations on R x R[symbol] with exponentially growing data -- ch. 16. Elements of calculus of pseudodifferential operators. 16.1. Basics of the theory of PDO with symbols of the class S[symbol]. 16.2. Operators depending on parameters. 16.3. Operators with symbols holomorphic in a tube domain. 16.4. Proofs of auxiliary technical results. 16.5. Change of variables and pricing of multi-asset contracts. 16.6. Pricing of barrier options under Lévy-like Feller processes. Finance Mathematical models. http://id.loc.gov/authorities/subjects/sh85048260 Finances Modèles mathématiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Finance Mathematical models fast Processos estocasticos. larpcal Processos gaussianos. larpcal Finanças (modelos matemáticos) larpcal Finance. rasuqam Option (Finances) rasuqam Modèle mathématique. rasuqam Levendorskiĭ, Serge, 1951- https://id.oclc.org/worldcat/entity/E39PCjJCFMQcrbwc8PTybG6f4m http://id.loc.gov/authorities/names/n90652806 Print version: Boyarchenko, Svetlana I. Non-Gaussian Merton-Black-Scholes theory. Singapore ; River Edge, NJ : World Scientific, 2002 9810249446 9789810249441 (DLC) 2002510652 (OCoLC)50323695 Advanced series on statistical science & applied probability ; v. 9. http://id.loc.gov/authorities/names/n97121977 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=210771 Volltext |
| spellingShingle | Boyarchenko, Svetlana I. Non-Gaussian Merton-Black-Scholes theory / Advanced series on statistical science & applied probability ; Ch. 1. Introduction. 1.1. The Gaussian Merton-Black-Scholes theory. 1.2. Regular Lévy processes of exponential type. 1.3. Pricing of contingent claims. 1.4. The generalized Black-Scholes equation. 1.5. Analytical methods used in the book. 1.6. An overview of the results covered in the book. 1.7. Commentary -- ch. 2. Lévy processes. 2.1. Basic notation and definitions. 2.2. Lévy processes: general definitions. 2.3. Lévy processes as Markov processes. 2.4. Boundary value problems for the Black-Scholes-type equation. 2.5. Commentary -- ch. 3. Regular Lévy Processes of Exponential type in ID. 3.1. Model classes. 3.2. Two definitions of regular Lévy processes of exponential type. 3.3. Properties of the characteristic exponents and probability densities of RLPE. 3.4. Properties of the infinitesimal generators. 3.5. A "naive approach" to the construction of RLPE or why they are natural from the point of view of the theory of PDO. 3.6. The Wiener-Hopf factorization -- ch. 4. Pricing and hedging of contingent claims of European type. 4.1. Equivalent Martingale measures in a Lévy market. 4.2. Pricing of European options and the generalized Black-Scholes formula. 4.3. Generalized Black-Scholes equation and its properties for different RLPE and different choices of EMM, and implications for parameter fitting. 4.4. Other European options. 4.5. Hedging. 4.6. Commentary -- ch. 5. Perpetual American options. 5.1. The reduction to a free boundary problem for the stationary generalized Black-Scholes equation. 5.2. Perpetual American put: the optimal exercise price and the rational put price. 5.3. Perpetual American call. 5.4. Put-like and call-like options: the case of more general payoffs. 5.5. Commentary -- ch. 6. American options: finite time horizon. 6.1. General discussion. 6.2. Approximations of the American put price. 6.3. American put near expiry -- ch. 7. First-touch digitals. 7.1. An overview. 7.2. Exact pricing formulas for first-touch digitals. 7.3. The Wiener-Hopf factorization with a parameter. 7.4. Price near the barrier. 7.5. Asymptotics as [symbol] -- ch. 8. Barrier options. 8.1. Types of barrier options. 8.2. Down-and-out call option without a rebate. 8.3. Asymptotics of the option price near the barrier. 8.4. Commentary -- ch. 9. Multi-asset contracts. 9.1. Multi-dimensional regular Lévy processes of exponential type. 9.2. European-style contracts. 9.3. Locally risk-minimizing hedging with a portfolio of several assets. 9.4. Weighted discretely sampled geometric average -- ch. 10. Investment under uncertainty and capital accumulation. 10.1. Irreversible investment and uncertainty. 10.2. The investment threshold. 10.3. Capital accumulation under RLPE. 10.4. Computational results. 10.5. Approximate formulas and the comparative statics -- ch. 11. Endogenous default and pricing of the corporate debt. 11.1. An overview. 11.2. Endogenous default. 11.3. Equity of a firm near bankruptcy level and the yield spread for junk bonds. 11.4. The case of a solvent firm. 11.5. Endogenous debt level and endogenous leverage. 11.6. Conclusion. 11.7. Auxiliary results. Ch. 12. Fast pricing of European options. 12.1. Introduction. 12.2. Transformation of the pricing formula for the European put. 12.3. FFT and IAC. 12.4. Comparison of FFT and IAC -- ch. 13. Discrete time models. 13.1. Bermudan options and discrete time models. 13.2. A perpetual American put in a discrete time model. 13.3. The Wiener-Hopf factorization. 13.4. Optimal exercise boundary and rational price of the option -- ch. 14. Feller processes of normal inverse Gaussian type. 14.1. Introduction. 14.2. Constructions of NIG-like Feller process via pseudodifferential operators. 14.3. Applications for financial mathematics. 14.4. Discussion and conclusions -- ch. 15. Pseudo-differential operators with constant symbols. 15.1. Introduction. 15.2. Classes of functions. 15.3. Space S'[symbol] of generalized functions on R[symbol]. 15.4. Pseudo-differential operators with constant symbols on R[symbol]. 15.5. The action of PDO in the Sobolev spaces on R[symbol]. 15.6. Parabolic equations. 15.7. The Wiener-Hopf equation on a half-line I. 15.8. Parabolic equations on [0,T] x R[symbol]. 15.9. PDO in the Sobolev spaces with exponential weights, in 1D. 15.10. The Sobolev spaces with exponential weights and PDO on a half-line. 15.11. Parabolic equations in spaces with exponential weights. 15.12. The Wiener-Hopf equation on a half-line II. 15.13. Parabolic equations on R x R[symbol] with exponentially growing data -- ch. 16. Elements of calculus of pseudodifferential operators. 16.1. Basics of the theory of PDO with symbols of the class S[symbol]. 16.2. Operators depending on parameters. 16.3. Operators with symbols holomorphic in a tube domain. 16.4. Proofs of auxiliary technical results. 16.5. Change of variables and pricing of multi-asset contracts. 16.6. Pricing of barrier options under Lévy-like Feller processes. Finance Mathematical models. http://id.loc.gov/authorities/subjects/sh85048260 Finances Modèles mathématiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Finance Mathematical models fast Processos estocasticos. larpcal Processos gaussianos. larpcal Finanças (modelos matemáticos) larpcal Finance. rasuqam Option (Finances) rasuqam Modèle mathématique. rasuqam |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85048260 |
| title | Non-Gaussian Merton-Black-Scholes theory / |
| title_auth | Non-Gaussian Merton-Black-Scholes theory / |
| title_exact_search | Non-Gaussian Merton-Black-Scholes theory / |
| title_full | Non-Gaussian Merton-Black-Scholes theory / Svetlana I. Boyarchenko, Sergei Z. Levendorskiĭ. |
| title_fullStr | Non-Gaussian Merton-Black-Scholes theory / Svetlana I. Boyarchenko, Sergei Z. Levendorskiĭ. |
| title_full_unstemmed | Non-Gaussian Merton-Black-Scholes theory / Svetlana I. Boyarchenko, Sergei Z. Levendorskiĭ. |
| title_short | Non-Gaussian Merton-Black-Scholes theory / |
| title_sort | non gaussian merton black scholes theory |
| topic | Finance Mathematical models. http://id.loc.gov/authorities/subjects/sh85048260 Finances Modèles mathématiques. MATHEMATICS Probability & Statistics Stochastic Processes. bisacsh Finance Mathematical models fast Processos estocasticos. larpcal Processos gaussianos. larpcal Finanças (modelos matemáticos) larpcal Finance. rasuqam Option (Finances) rasuqam Modèle mathématique. rasuqam |
| topic_facet | Finance Mathematical models. Finances Modèles mathématiques. MATHEMATICS Probability & Statistics Stochastic Processes. Finance Mathematical models Processos estocasticos. Processos gaussianos. Finanças (modelos matemáticos) Finance. Option (Finances) Modèle mathématique. |
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