In this paper we propose semi-closed-form solutions, subject to an inversion of the Fourier transform, for the price of VIX options and target volatility options (TVOs) under affine GARCH models based on Gaussian and Inverse Gaussian distributions. We illustrate the advantage of the proposed...

We propose an explicit closed-form approximation formula for the price of discretely monitored single or double barrier options whose underlying asset evolves according to a generic one-dimensional Markov process. This set of stochastic processes includes, but is not limited to, diffusion and...

Recently, Cai et al. (2015) proposed closed-form double transform approxima- tion formulas for prices of both discretely and continuously monitored Asian options under the setting of a general continuous-time Markov chain. In this note, we analytically invert the Z−transform and the Laplace...

In this paper, we develop a Markov chain-based approximation method to price arithmetic Asian options for short maturities under the case of geometric Brownian motion. It has the advantage of being a closed-form approximation involving only matrices. It is an accurate, efficient, and stable...

In this paper, we construct tight lower and upper bounds for the price of an American strangle, which is a special type of strangle consisting of long positions in an American put and an American call, where the early exercise of one side of the position will knock-out the remaining side. This...

In this paper, we extend the lower-upper bound approximation (LUBA) idea of Broadie and Detemple [Broadie, M., Detemple, J., (1996) American option valuation: New bounds, approximations, and comparison of existing methods. Review of Financial Studies. 9(4): 1211-1250] to the Laplace space. We...

The stochastic alpha beta rho (SABR) model introduced by Hagan et al. (2002) is widely used in both fixed income and the foreign exchange (FX) markets. Continuously monitored barrier option contracts are among the most popular derivative contracts in the FX markets. In this paper, we develop...

In this paper, we discuss a newly introduced exotic derivative called the “Timer Option”. Instead of being exercised at a fixed maturity date as a vanilla option, it has a random date of exercise linked to the accumulated variance of the underlying stock. Unlike common...

This paper establishes the second-order convergence rates of the continuous-time Markov chain (CTMC) approximation method for pricing continuously monitored occupation time derivatives (step options, conditional Asian options) and arithmetic Asian options and their Greeks. We fill the gap in the...

In this paper, we derive a closed-form explicit model-free formula for the (Black-Scholes) implied volatility. The method is based on the novel use of the Dirac Delta function, corresponding delta families, and the change of variable technique. The formula is expressed through either a limit or...