A simple analytics framework for evaluating mean escape time in different term structures with stochastic volatility

This article considers a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlations between the underlying assets, as well as between their volatilities. The model accounts for the existence of correlation term structure and correlation skew. The article shows that the Wishart specification can generate different patterns corresponding to the correlation skew for a wide range of correlation term structures. Another advantage of the model is that it is analytically tractable and, hence, it is possible to obtain semi-closed-form solutions for the prices of plain vanilla options, as well as for the price of exotic derivatives. In this sense, this article develops semi-closed-form formulas for the price of European worst-of options with barriers and/or forward-start features. To motivate the introduction of the Wishart volatility model, the article compares the prices obtained under this model and under a multi-asset stochastic volatility model with constant instantaneous correlations. The results reveal the existence of a stochastic correlation premium and show that the consideration of stochastic correlation is a key element for the valuation of these structures.

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Pricing of Swaptions in Affine Term Structures with Stochastic Volatility

Applied and Numerical Harmonic Analysis - Advances in Mathematical Finance ◽

10.1007/978-0-8176-4545-8_10 ◽

2007 ◽

pp. 173-193 ◽

Cited By ~ 2

Author(s):

Michael Heidari ◽

Alil Hirsa ◽

Dilip B. Madan

Keyword(s):

Stochastic Volatility ◽

Term Structures

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Extensions

Yield Curve Modeling and Forecasting ◽

10.23943/princeton/9780691146805.003.0004 ◽

2013 ◽

Author(s):

Francis X. Diebold ◽

Glenn D. Rudebusch

Keyword(s):

Bayesian Analysis ◽

Stochastic Volatility ◽

Research Program ◽

Functional Form ◽

Credit Spreads ◽

Bond Yields ◽

Ongoing Research ◽

Factor Loadings ◽

Term Structures ◽

Macroeconomic Fundamentals

This chapter highlights aspects of the vibrant ongoing research program associated with the ideas developed in earlier chapters. It begins with a collage-style sketch of work involving Bayesian analysis, functional form for factor loadings, term structures of credit spreads, and nonlinearities. It then discusses in greater detail the incorporation of more than three yield factors. Next, it treats stochastic volatility in both dynamic Nelson–Siegel model (DNS) and arbitrage-free DNS (AFNS) environments, with some attention to the issue of unspanned stochastic volatility. Finally, it discusses the incorporation of macroeconomic fundamentals in their relation to bond yields. It also introduces aspects of modeling real versus nominal yields in DNS/AFNS environments, a theme treated in detail in Chapter 5.

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