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Stochastic Interest Rates for Local Volatility Hybrid Models: Wilmott Magazine Article
E. Benhamou, A. Gruz and A. Rivoira 59 Views

This paper studies the impact of stochastic interest rates for local volatility hybrids. We first show that we can explicitly determine the bias between the local volatility of a model with stochastic interest rates and the local volatility of the same model but with deterministic interest rates as a function between the correlation of the stochastic interest rates and the digital at the local strike.


A Perfect Calibration! Now What?: Wilmott Magazine Article
Wim Schoutens, Erwin Simons & Jurgen Tistaert 3752 Views

We show that several advanced equity option models incorporating stochastic volatility can be calibrated very nicely to a realistic option surface. More specifically, we focus on the Heston Stochastic Volatility model (with and without jumps in the stock price process), the Barndorff-Nielsen-Shephard model and LÚvy models with stochastic time. All these models are capable of accurately describing the marginal distribution of stock prices or indices and hence lead to almost identical European vanilla option prices. As such, we can hardly discriminate between the different processes on the basis of their smile-conform pricing characteristics. We therefore are tempted applying them to a range of exotics. However, due to the different structure in path-behaviour between these models, the resulting exotics prices can vary significantly. It motivates a further study on how to model the fine stochastic behaviour of assets over time.

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