We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density...

Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating risk-neutral densities associated with several maturities. Our method uses bicubic splines in order to achieve the desired smoothness f...

Option price data is often used to infer risk-neutral densities for future prices of an underlying asset. Given the prices of a set of options on the same underlying asset with different strikes and maturities, we propose a nonparametric approach for estimating the evolution of the risk-neutral density in time. Our method uses bicubic splines in order to achieve the desired smoothness for the e...

One option-pricing problem that has hitherto been unsolved is the pricing of a European call on an asset that has a stochastic volatility. This paper examines this problem. The option price is determined in series form for the case in which the stochastic volatility is independent of the stock price. Numerical solutions are also produced for the case in which the volatility is correlated with t...

The Real Option Theory (OR) offers a modern methodology for the valuation of an investment project because it considers the value of managerial flexibility facing project uncertainties. The present work seeks to study the deferral option value for a polypropylene petrochemical plant investment project. Perhaps the most critical step of OR is the estimation of the project volatility. This work e...

We study the perpetual American call option pricing problem in a model of a financial market in which the firm issuing a risky 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 prices available from the market. The asset price dynamics are described by a geometric Brownian motion wit...

One method to compute the price of an arithmetic Asian option in a Lévy driven model is based on the exponential functional of the underlying Lévy process: If we know the distribution of the exponential functional, we can calculate the price of the Asian option via the inverse Laplace transform. In this paper we consider pricing Asian options in a model driven by a general meromorphic Lévy proc...

Recall that the American option has strike K and maturity T and gives the holder the right to exercise at any time in [0, T ]. The American option is not straightforward to price in the Monte Carlo framework that we have discussed. The reason is that the derivative cash flow function f(S, t) is not well defined. The problem is that we cannot compute the derivative cash flow until we know how th...

This paper studies modeling and existence issues for market models of option prices in a continuous-time framework with one stock, one bond and a family of European call options for one fixed maturity and all strikes. After arguing that (classical) implied volatilities are ill-suited for constructing such models, we introduce the new concepts of local implied volatilities and price level. We sh...

In this paper, we provide a new proof of the result that option prices are increasing in volatility when the underlying is a diffusion process. This has been shown to hold for convex payoff, path-independent options by El Karoui et al [7], Hobson [12] amongst others. The advantage of the new proof is that it can be extended to establish monotonicity results for path-dependent payoffs where the ...