Speaker(s): Hailiang Yang (University of Hong Kong)
This work is motivated by the valuation problem of Guaranteed Minimum Death Benefits in various equity-linked products. At the time of death, a benefit payment is due. It may depend not only on the price of a stock or stock fund at that time, but also on prior prices. The problem is to calculate the expected discounted value of the benefit payment. Because the distribution of the time of death can be approximated by a combination of exponential distributions, it suffices to solve the problem for an exponentially distributed time of death. We model the stock price as the exponential of a Brownian motion or Brownian motion plus an independent compound Poisson process.
Results for exponential stopping of Brownian motion and exponential stopping of a Levy process are used to derive a series of closed-form formulas for a variety of contingent call and put options, lookback options, and barrier options with one or two barriers.