A knock-in American option under a trigger clause is an option contract in which the option holder receives an American option conditional on the underlying stock price breaching a certain trigger level (also called barrier level). We present analytic valuation formulas for knock-in American options under the Black-Scholes pricing framework. The price formulas possess different analytic represe...

a r t i c l e i n f o This paper reexamines the liquidity effect on stock expected returns in the NYSE over the period 1926–2008, the pre-1963 period, for which there is a lack of research, and the post-1963 period. The results from the entire sample of 1926–2008 show that expected returns increase with the stock level illiquidity. However, illiquidity level has explanatory power in the cross-s...

Identi cation of patterns in stock markets has been an important subject for many years. In the past, numerous techniques, both technical and econometric, were used to predict changes in stock markets, but dependences among all the companies listed on a stock market were considered in a limited extent. Numerous studies con rm that larger stocks items appear to in uence smaller ones and that, on...

In the framework of bilateral Gamma stock models we seek for adequate option pricing measures, which have an economic interpretation and allow numerical calculations of option prices. Our investigations encompass Esscher transforms, minimal entropy martingale measures, p-optimal martingale measures, bilateral Esscher transforms and the minimal martingale measure. We illustrate our theory by a n...

Closed solutions to the problem of pricing a Russian option when the stock is modeled by a diffusion with negative jumps are obtained. The Russian option is a perpetual American option on the maximum value of the stock. That stock is assumed to have the form of a Wiener process with drift and negative mixed–exponentially distributed jumps driven by a Poisson process. This result generalizes tho...

The nance industry is beginning to adopt parallel computing for numerical computation, and will soon be in a position to use parallel supercomputers. This paper examines software issues and performance of a stock option pricing model running on the Connection Machine-2 and DECmpp-12000. Pricing models incorporating stochastic volatility with American call (early exercise) are computationally in...

The aim of this thesis is to investigate the mathematics of Markov-modulated models for derivatives pricing. We consider a model where instantaneous stock volatility and drift are driven by a continuous time finite Markov chain. We present a new derivation of an integral representation for attainable non-path dependent options’ prices in a twostate and three-state Markov chain model, and comput...

This paper develops the method for pricing bivariate contingent claims under General Autoregressive Conditionally Heteroskedastic (GARCH) process. In order to provide a general framework being able to accommodate skewness, leptokurtosis, fat tails as well as the time varying volatility that are often found in financial data, generalized hyperbolic (GH) distribution is used for innovations. As t...

We study the performance of conditional asset pricing models in explaining the German cross-section of stock returns. Our test assets are portfolios sorted by size and book-to-market as in the paper by Fama and French (1993). Our results show that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved substantially when allowing for time-varying parameters of the st...

This paper presents a model for option pricing in markets that experience financial crashes. The stochastic differential equation (SDE) of stock price dynamics is coupled to a post-crash market index. The resultant SDE is shown to have stock price and time dependent volatility. The partial differential equation (PDE) for call prices is derived using risk-neutral pricing. European call prices ar...