The drawdown in the price of an asset shows how much the price falls relative to its historical maximum. This paper considers the pricing problem of American style drawdown call options, which allow the holder to optimally choose the time to receive a call payoff written on the drawdown. Our...

This paper proposes a novel approach for pricing discretely monitored multi-asset barrier options and computing joint survival probability in multivariate exponential Levy asset price models. We calculate the Fourier transform of appropriately dampened value functions recursively using...

This paper develops an eigenfunction expansion approach to solve discretely monitored first passage time problems for a rich class of Markov processes, including diffusions and subordinate diffusions with jumps, whose transition or Feynman-Kac semigroups possess eigenfunction expansions in L2...

We propose an efficient method to evaluate callable and putable bonds under a wide class of interest rate models, including the popular short rate diffusion models, as well as their time changed versions with jumps. The method is based on the eigenfunction expansion of the pricing operator....

We develop a data-driven approach for options market making. Using stock options data from CBOE, we find that both buy and sell orders exhibit strong self-excitation but insignificant cross-excitation. We show that a Hawkes process with a time-varying baseline intensity and the power law kernel...