Determining Volatility Surfaces and Option Values From an Implied Volatility Smile

@inproceedings{Carr1998DeterminingVS,
  title={Determining Volatility Surfaces and Option Values From an Implied Volatility Smile},
  author={Peter Carr and D. Madan and Morgan Stanley Dean Witter and Robert H. Smith},
  year={1998}
}
Using only the implied volatility smile of a single maturity T and an assumption of path-independence, we analytically determine the risk-neutral stock price process and the local volatility surface up to an arbitrary horizon T 0 T . Our path-independence assumption requires that each positive future stock price St is a function of only time t and the level Wt of the driving standard Brownian motion (SBM) for all t 2 (0; T 0). Using the T maturity option prices, we identify this stock pricing… CONTINUE READING