TITLE:           A Stochastic Elasticity Correction to the Black-Scholes Formula

SPEAKER:         Professor Jeong-Hoon Kim (Yonsei University, Korea)
TIME/DATE:      4pm, Monday, 11 July
VENUE:  Room 6115 (OGGB)

About the Speaker

Professor Kim is specialist in the mathematics of asset pricing, and is based in the Financial Mathematics Lab at Yonsei University. He is presently on sabbatical in Australasia, and will be visiting the CMSS until 17 July.   He is in room 6101 of the OGGB if you would like to drop by and say hello.  Professor Kim’s talk will discuss a generalisation of the Black-Scholes formula which introduces a type of stochastic volatility.  A more detailed abstract appears below.  Professor Kim has promised to emphasise the financial/economic logic behind the ideas, so the talk will be accessible to the less mathematically inclined!

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Abstract:
We propose a CEV-type model where the elasticity takes a perturbative form in terms of a small and fast mean-reverting process. Based on this multiscale hybrid structure of the volatility of the underlying asset price, we study option pricing in such a way that the resultant option price has a desirable correction to the Black-Scholes formula. The correction effects are developed by asymptotic analysis based upon the Ornstein-Uhlenbeck diffusion that decorrelates rapidly while fluctuating on a fast time-scale. Our results show that the implied volatilities demonstrate a smile effect (right geometry), which overcomes the major drawback of the Black-Scholes model, and move to the right direction as the underlying asset price increases (right dynamics), which fits observed market behavior and removes the possible instability of hedging that local volatility models might cope with. We also show correction effects on the fitting of the implied volatility surface to the market data as well as on the reduction of the hedging cost.