Related papers: Local Volatility Pricing Models for Long-dated FX …
When trading American and Asian options in the FX derivatives market, banks must calculate prices using a complex mathematical model. It is often observed that different models produce varying prices for the same exotic option, which…
We propose Monte Carlo calibration algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and finally stochastic local volatility with stochastic interest…
We present a stochastic local volatility model for derivative contracts on commodity futures. The aim of the model is to be able to recover the prices of derivative claims both on futures contracts and on indices on futures strategies.…
We derive generalizations of Dupire formula to the cases of general stochastic drift and/or stochastic local volatility. First, we handle a case in which the drift is given as difference of two stochastic short rates. Such a setting is…
Based on the existing literature, this article presents the different ways of choosing the parameters of stochastic volatility models in general, in the context of pricing financial derivative contracts. This includes the use of stochastic…
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential…
We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX…
We investigate the problem of pricing derivatives under a fractional stochastic volatility model. We obtain an approximate expression of the derivative price where the stochastic volatility can be composed of deterministic functions of time…
We introduce a local volatility model for the valuation of options on commodity futures by using European vanilla option prices. The corresponding calibration problem is addressed within an online framework, allowing the use of multiple…
This paper proposes a numerical method for pricing foreign exchange (FX) options in a model which deals with stochastic interest rates and stochastic volatility of the FX rate. The model considers four stochastic drivers, each represented…
We study a market model in which the volatility of the stock may jump at a random time from a fixed value to another fixed value. This model was already described in the literature. We present a new approach to the problem, based on partial…
Local Volatility (LV) is a powerful tool for market modeling, enabling the generation of arbitrage-free scenarios calibrated to all European options. To implement LV, we need to interpolate and extrapolate option prices. This approach is…
This paper addresses the approximation of the local volatility function in the Cheyette interest rate model. Its main contribution is an explicit analytical formula for approximating local volatility, derived by extending the classical…
We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…
Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually…
This article presents a generic hybrid numerical method to price a wide range of options on one or several assets, as well as assets with stochastic drift or volatility. In particular for equity and interest rate hybrid with local…
Local Stochastic Volatility (LSV) models have been used for pricing and hedging derivatives positions for over twenty years. An enormous body of literature covers analytical and numerical techniques for calibrating the model to market data.…
We discuss the possibility of obtaining model-free bounds on volatility derivatives, given present market data in the form of a calibrated local volatility model. A counter-example to a wide-spread conjecture is given.
What is the dominating mechanism of the price dynamics in financial systems is of great interest to scientists. The problem whether and how volatilities affect the price movement draws much attention. Although many efforts have been made,…
This article provides a list of counterexamples, where some of the popular fx option interpolations break down. Interpolation of FX option prices (or equivalently volatilities), is key to risk-manage not only vanilla FX option books, but…