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Option Pricing with Stochastic Volatility

DOI: 10.4236/jamp.2015.312189, PP. 1645-1653

Keywords: Contingent Claim, Stochastic Volatility, Ito’s Lemma, Cauchy problem, Bivariate

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Abstract:

The study analyses some problems arising in stochastic volatility models by using Ito’s lemma and its applications to boundary Cauchy problem by giving the solution of vanilla option pricing models satisfying the partial differential equation obtained by assuming stochastic volatility in replication problems and risk neutral probability.

References

[1]  Heston, S.L. (1993) A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options. Review of Financial Studies, 6, 327-343.
http://dx.doi.org/10.1093/rfs/6.2.327
[2]  Black, F. and Scholes, M. (1973) The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81, 637-654.
http://dx.doi.org/10.1086/260062
[3]  Dell’Era, M. (2011) Geometrical Approximation Method and Stochastic Volatility Market Models. International Review of Applied Financial Issues and Economics.
[4]  Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A Theory of the Term Structure of Interest Rates. Econometrica, 53, 385-407.
http://dx.doi.org/10.2307/1911242
[5]  Heath, D., Jarrow, R. and Morton. A. (1992) Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation. Econometrica, 60, 77-105.
http://dx.doi.org/10.2307/2951677
[6]  Bjork, T. (1999) Arbitrage Theory in Continuous Time. Oxford University Press, Oxford.
[7]  Alexander, C. (2008) Pricing, Hedging and Trading Financial Instruments. John Wiley & Sons, New York.

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