Option pricing
Last option before the armageddon
Damiano Brigo and Massimo Morini show how the pricing of credit index options depends on the probability of a financial portfolio 'armageddon'. They introduce a new equivalent pricing measure that lays the foundation for a market model framework in multi…
Stepping through Fourier space
Diverse finite-difference schemes for solving pricing problems with Levy underlyings appear in financial literature. Invariably, the integral and diffusive terms are treated asymmetrically, large jumps are truncated, and the methods are difficult to…
Right time to overwrite
Call overwriting
Information derivatives
Andrei Soklakov considers the problem of creating derivatives to provide tailored exposure to volatility risk. Information theory leads us to a whole class of such products. This class of 'information derivatives' includes the standard volatility…
Information derivatives
Andrei Soklakov considers the problem of creating derivatives to provide tailored exposure to volatility risk. Information theory leads us to a whole class of such products. This class of 'information derivatives' includes standard volatility products -…
A short cut to the rainbow
Per Horfelt designs an efficient and accurate method to price many popular multi-asset options such as options on the minimum and maximum of several assets and podiums. The method is based on a modification of the conditional independence model and is…
Information derivatives
This paper considers the problem of creating derivatives to provide tailored exposure to volatility risk
Vix option pricing in a jump-diffusion model
Artur Sepp discusses Vix futures and options and shows that their market prices exhibit positive volatility skew. To better model the market behaviour of the S&P 500 index and its associated volatility skew, he introduces the stochastic dynamics of the…
Information derivatives
Andrei Soklakov considers the problem of creating derivatives to provide tailored exposure to volatility risk. Information theory leads us to a whole class of such products. This class of 'information derivatives' includes the standard volatility…
Calibrating and pricing with local volatility models
Cutting edge - Option pricing
Calibrating and pricing with embedded local volatility models
Consistently fitting vanilla option surfaces when pricing volatility derivatives such as Vix options or interest rate/equity hybrids is an important issue. Here, Yong Ren, Dilip Madan and Michael Qian Qian show how this can be accomplished, using a…
Pricing with a smile
In the January 1994 issue of Risk, Bruno Dupire showed how the Black-Scholes model can be extended to make it compatible with observed market volatility smiles, allowing consistent pricing and hedging of exotic options
Realised volatility and variance: options via swaps
Peter Carr and Roger Lee present explicit and readily applicable formulas for valuing options on realised variance and volatility. They use variance and volatility swaps - or alternatively vanilla options - as pricing benchmarks and hedging instruments…
Markovian projection for volatility calibration
Vladimir Piterbarg looks at the Markovian projection method, a way of obtaining closed-form approximations of European-style option prices on various underlyings that, in principle, is applicable to any (diffusive) model. The aim is to distil the essence…
Realised volatility and variance: options via swaps
Volatility Options
Markovian projection for volatility calibration
Vladimir Piterbarg looks at the 'Markovian projection method', a way of obtaining closed-form approximations of European-style option prices on various underlyings that, in principle, is applicable to any (diffusive) model. The aim is to distil the…
The vanna-volga method for implied volatilities
Cutting Edge - Option pricing
Maximum draw-down and directional trading
Maximum draw-down measures the worst drop in a market in a given time period. Jan Vecer shows how to price and replicate this event. Replication can be naturally linked to existing popular trading strategies, such as momentum or contrarian trading
Maximum draw-down and directional trading
Maximum draw-down measures the worst drop in a market in a given time period. Jan Vecer shows how to price and replicate this event. Replication can be naturally linked to existing popular trading strategies, such as momentum or contrarian trading
Variance swaps and non-constant vega
Variance swaps have gained in popularity due to their ability to provide investors with purevolatility exposure – a fairly stable gamma exposure despite changes in the value of theunderlying. The vega exposure of this product, however, varies linearly…
Smile dynamics II
In an article published in Risk in September 2004, Lorenzo Bergomi highlighted how traditionalstochastic volatility and jump/Lévy models impose structural constraints on the relationshipbetween the forward skew, the spot/volatility correlation and the…
Smile dynamics
Traditionally, smile models have been assessed according to how well they fit market option prices across strikes and maturities. However, the pricing of most recent exotic structures, such as reverse cliquets or Napoleons, is more dependent on the…