In this talk, we will discuss two topics:
Volatility of an underlying security is a key parameter in the Black-Scholes theory for pricing options. Therefore it is important to develop an efficient method to estimate the volatility using historical data. In this talk, a volatility estimator based on multiple periods of high, low, open and close prices is presented. The new estimator has the following nice properties: (a) it is unbiased in the continuous limit; (b) it deals with opening price jumps in a consistent way; (c) it is independent of the drift of the underlying security; (d) its variance is the smallest among all estimators with the similar properties (e.g. the classical estimator based on closing prices only). The improvement of accuracy could be dramatic under certain conditions, namely the result of the new estimator using only two day's data will have the same accuracy as that of the classical close-to-close estimator using three week's data. This is a joint work with Dr. Dennis Yang at Clearview Trading.
We present analytical approximate solutions for the critical prices and the values of American barrier options and American lookback strike options. In barrier options, one specifies a barrier. Once the value of the underlying asset reaches the barrier, the öut" barrier option becomes worthless and the ïn" barrier option becomes alive. Lookback options are path-dependent options whose payoff depends on the maximum or the minimum realized value of the underlying asset over the life of the option. Our theoretical predictions for the critical prices and the values of these American exotic options are in excellent agreement with the results obtained from direct numerical computations. This is a joint work with Dr. Tanya Taksar at Fiduciary Trust.