In this article we study the price of an American style option based on hedging the underlying assets at discrete time. Like its European style analog, the value of the option is not given in general by an expectation with respect to an equivalent martingale measure. We provide the optimal...

The construction of martingales with given marginal distributions at given times is a recurrent problem in financial mathematics. From a theoretical point of view, this problem is well-known as necessary and sufficient conditions for the existence of such martingales have been described....

We study the perpetual American call option pricing problem in a model of a financial market in which the firm issuing a traded asset can regulate the dividend rate by switching it between two constant values. The firm dividend policy is unknown for small investors, who can only observe the...

We investigate the effect of including variance derivatives as calibration and hedging instruments for pricing and hedging exotic structures. This is studied empirically using market data for SPX and VIX derivatives applied in a stochastic volatility jump diffusion model

U.S. exchange-traded stock options are exercisable before expiration. While put options should frequently be exercised early to earn interest, they are not. In this paper, we derive an early exercise decision rule and then examine actual exercise behavior during the period January 1996 through...

We reviewed (extended and made more compact/self-explained) some formulas, previously appeared in the literature, for the evaluation of equity options and bond options in the Leland model (1994), where stockholders have a perpetual American option to default.Our formulas have been expressed in...

We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the investor and the market value the options by risk-neutral...

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...

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...