Market option prices in last 20 years confirmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomial trees (IBT) models capture the variations of the implied volatility known as volatility smile. They provide a discrete...

We suggest a semi-nonparametric estimator for the entire call price surface based on a tensor-product B-spline. To enforce no-arbitrage constraints in strike and calendar dimensions we establish sufficient no-arbitrage conditions on the control net of the tensor product (TP) B-spline. Since...

Implied and local volatility are very important variables to market practitioners because such variables can be exploited in numerous option models for the pricing and hedging of diverse exotic options. In the present study, we propose a method to implement no-arbitrage constraints in estimating...

There are two unique volatility surfaces associated with any arbitrage-free set of standard European option prices, the implied volatility surface and the local volatility surface. Several papers have discussed the stochastic differential equations for implied volatilities that are consistent...

Convertible bonds are hybrid securities whose pricing relies on a set of complex inter-dependencies due to the sensitivity to interest rate risk, underlying (equity) risk, FX risk, and credit risk, and due to the convertible bond’s early exercise American feature. We present a two factor model...

Market option prices in last 20 years conrmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomial trees (IBT) models capture the variations of the implied volatility known as \volatility smile". They provide a discrete...

Convertible bonds are hybrid securities whose pricing relies on a set of complex inter-dependencies due to the sensitivity to interest rate risk, underlying (equity) risk, FX risk, and credit risk, and due to the convertible bond’s early exercise American feature. We present a two factor model...

In this paper we recover the Black-Scholes and local volatility pricing engines in the presence of an unspecified, fully stochastic volatility. The input volatility functions are allowed to fluctuate randomly and to depend on time to expiration in a systematic way, bringing the underlying theory...

A new method for pricing contingent claims based on an asymptotic expansion of the dynamics of the pricing density is introduced. The expansion is conducted in a preferred coordinate frame, in which the pricing density looks stationary. The resulting asymptotic Kolmogorov-backward-equation is...

A new method for pricing contingent claims based on an asymptotic expansion of the dynamics of the pricing density is introduced. The expansion is conducted in a preferred coordinate frame, in which the pricing density looks stationary. The resulting asymptotic Kolmogorov-backward-equation is...