We show that if the discounted Stock price process is a continuous martingale, then there is a simple relationship linking the variance of the terminal Stock price and the variance of its arithmetic average. We use this to establish a model-independent upper bound for the price of a continuously...

In this paper we prove an approximate formula expressed in terms of elementary functions for the implied volatility in the Heston model. The formula consists of the constant and first order terms in the large maturity expansion of the implied volatility function. The proof is based on...

We present a quasi-analytical method for pricing multi-dimensional American options based on interpolating two arbitrage bounds, along the lines of Johnson (1983). Our method allows for the close examination of the interpolation parameter on a rigorous theoretical footing instead of empirical...

The paper develops an efficient Monte Carlo method to price discretely monitored Parisian options based on a control variate approach. The paper also modifies the Parisian option design by assuming the option is exercised when the barrier condition is met rather than at maturity. We obtain...

Recently, simulation methods combined with regression techniques have gained importance when it comes to American option pricing. In this paper we consider such methods and we examine numerically their convergence properties. We first consider the Least Squares Monte-Carlo (LSM) method of...

In this article we give a lower bound approximation to a stochastic program that is typical for many complex financial derivatives, e.g. Bermudan options, Rainbow options and swing contracts. The approximation is based on an algorithm that does not require any simulation but uses a well-known...

Financial markets exhibit high levels of volatility. Volatile markets are usually associated with high risks and uncertain investment returns. Financial institutions therefore, usually opt to hedge their investment portfolios against the high volatility using a suitable hedging structure. One...

This paper describes an empirical study of the information content of daily share prices and American put and call option mid-quotes about their generating process. Considering stock return and its volatility as the risk factors and without parameterizing their historical joint dynamics, two...

This paper empirically examines whether asset's liquidity can help resolve the known strike-price biases of the Black-Scholes model for different liquidity measures based on trading volume, bid-ask spread and the Amihud's ILLIQ. Our results indicate that, when the underlying asset or its...

Asian options are securities with a payoff that depends on the average of the underlying stock price over a certain time interval. We identify three natural assets that appear in pricing of the Asian options, namely a stock S, a zero coupon bond BT with maturity T, and an abstract asset A (an...