In this paper, we present our study on a hybrid stochastic volatility model incorporating local volatility for pricing options in the foreign exchange (FX) market. The hybrid stochastic-local volatility model (SLV) could match the implied volatility surface well and meanwhile shows the...

Managed synthetic CDOs permit the dynamic substitution of credits in the reference portfolio. The expectation of investors in is that a skilled manager should be able to identify deteriorating credits before they experience a credit event and should therefore be able to remove the credit from...

In this paper, we consider an evolution non local free boundary problem that arises in the modeling of speculative bubbles. The solution of the model is the speculative component in the price of an asset. In the framework of viscosity solutions, we show the existence and uniqueness of the...

Traditional valuation tools such as discounted cash flow (DCF) models fail in valuing research and development (R&D)-intensive pharmaceutical firms adequately because most of the market value of the firm is embedded in unexercised real options whose future value is uncertain at this moment. From...

We consider implied volatility, time-dependent volatility, local volatility and stochastic volatility. We derive relationships between the different concepts. The relationships are of an exact analytical type if this is possible, else we use expansions to obtain approximate expressions. We close...

We build on of the work of Henry-Labordµere and Lewis on the small-time behaviour of the return distribution under a general local-stochastic volatility model with zero correlation. We do this using the Freidlin-Wentzell theory of large deviations for stochastic differential equations, and then...

Using the Gartner-Ellis theorem from large deviation theory, we characterize the leading-order behaviour of call option prices under the Heston model, in a new regime where the maturity is large and the log-moneyness is also proportional to the maturity. Using this result, we then derive the...

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 propose a novel approach of solving and analyzing linear rational expectations models with endogenous information frictions. Our approach is build upon policy function iterations in the frequency domain. We develop the theoretical framework of this approach using rational approximations,...