In some papers we remarked that derivation of the Black Scholes Equation (BSE) contains mathematical ambiguities. In particular, there are two problems which can be raised by accepting Black Scholes (BS) pricing concept. One is technical derivation of the BSE and the other the pricing definition...

We propose an efficient pricing method for arithmetic Asian options based on Fourier-cosine expansions. In particular, we allow for mean reversion and jumps in the underlying price dynamics. There is an extensive body of empirical evidence in the current literature that points to the existence...

The derivation of Asian option value has posed a challenge to financial mathematicians for the last two decades. Fu, Madan and Wang (1999) made a comparison between the Laplace transform approach and the Monte Carlo approach, and found that the numerical inversion method encountered severe...

By exploiting the flexibility of the Wishart process, we propose an application of this framework to the pricing of Chicago Board Options Exchange (CBOE) volatility index (VIX) options. Our methodology is analytically tractable and yet flexible enough to efficiently price CBOE VIX options. In...

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...

The objective of this paper is to perform a joint analysis of jump activity for commodities and their respective volatility indices. Exploiting the property that for affine jump-diffusion models a volatility index, which is quoted on the market, is an affine function of the instantaneous...

This report provides an overview of the utility of single stock and custom basket options in fund management. It is shown that managers of active equity funds can limit possible negative return contributions of their over - and underweight positions via single stock options and thus help to...

Option pricing literature is usually concerned with financial contracts whose payoffs depend on decisions by only one of the contract's parties. Generalizations to more complex cases with decisions by both parties are impeded by the ad-hoc nature of many contributions. One prominent example...

Given the competitiveness of a market-making environment, the ability to speedily quote option prices consistent with an ever-changing market environment is essential. Thus, the smallest acceleration or improvement over traditional pricing methods is crucial to avoid arbitrage. We propose a...

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...