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Presentations

Volatility Smiles in Commodity Futures

Qimou Su, Director, Quantitative & Risk Analytics, gave a presentation at Global Derivatives USA  in Chicago. The talk, titled "Volatility Smiles in Commodity Futures" featured:

• Multi-factor commodity model with explicit modeling of volatility smiles
• Volatility interpolation and calibration of implied marginal distributions
• Separation of volatility smiles and correlation calibrations
• Simulation algorithm based on copula techniques to value path-dependent options

Papers

Incorporating Overhedges in SciFinance PDE and Monte Carlo Models

SciFinance allows users to incorporate over(under) hedges of arbitrary characteristics into synthesized PDE, Monte Carlo, and GPU-enabled Monte Carlo code. Users can call existing library functions in SciFinance-synthesized code for most any purpose, overhedges being just one example.

Barriers, which create discontinuities payoffs, coupons and other cashflows, are common features of financial products. As spot prices approach barriers, hedging parameters such as deltas, gammas and vegas can become extremely volatile. In theory, hedge rebalances need to be frequent and large with concomitantly large transaction costs. Consequently, such products are frequently booked and hedged as option spreads, which smooth discontinuities, limiting deltas and gammas, and thereby reducing hedging costs.

Putting Smiles Back to the Futures

The research paper "Putting Smiles Back to The Futures" describes a practical method to extend the classical log-normal Gabillon model to incorporate volatility smiles; and a forward market model for pricing options on Forward Freight Agreements (FFA) with a term structure of FFA volatility.

Gabillon Model with Volatility Smiles

The Gabillon model can effectively capture the difference in future curve volatility between the front- and back-ends of the curve. However, the Gabillon model ignores the effects of volatility smiles that are commonly observed in the options markets. Given their dependency on multiple points of the futures curve, the value of many commodity derivatives can be sensitive to the volatility smiles of futures prices. To effectively price and risk manage these products, we need to incorporate smile information into the correlation and term structure modeling of the futures curve.

Construction of Volatility Surface for Commodity Futures

Multi-factor lognormal models such as Gabillon and Smith-Schwartz ignore the effects of volatility smiles commonly observed in the options markets. We present a practical, robust method for extending classical lognormal models to incorporate volatility smiles.

Volatility smile calibration and better volatility surface construction improves the accuracy of derivatives valuations:

• Calibration of volatility term structure and volatility smiles
• Construction of arbitrage-free volatility surfaces and marginal distributions
• Robust and accurate algorithms to construct local volatility surfaces
• Separation of Samuelson effect, volatility smiles and correlations
• Simulation algorithm based on copula techniques to value path-dependent options