Asymptotic Analysis of Option Pricing Functions
This chapter introduces call and put pricing functions in general asset price models. The chapter first takes up the question of what are the conditions under which a function of two variables (strike price and maturity) is a call pricing function. The answer to this question is given in the form of a characterization theorem for general call pricing functions. The best known call pricing function is without doubt the pricing function in the Black-Scholes model. This celebrated model is discussed in the present chapter and an analytical proof of the Black-Scholes formula is given. Moreover, sharp asymptotic formulas are obtained for call pricing functions in the Hull-White, Stein-Stein, and Heston models.
KeywordsAsset Price Option Price Price Function Stochastic Volatility Model Scholes Model
- [BH95]Bleistein, N., Handelsman, R. A., Asymptotic Expansions of Integrals, Holt, Rinehart and Winston, New York, 1995. Google Scholar
- [RY04]Revuz, D., Yor, M., Continuous Martingales and Brownian Motion, Springer, Berlin, 2004. Google Scholar
- [Rop10]Roper, M., Arbitrage free implied volatility surfaces, preprint, 2010. Google Scholar