Technical paper/Option pricing
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…
Local cross-entropy
One way of addressing the inconsistency between exchange-traded options prices and the Black-Scholes model is to attempt to find alternative risk-neutral distributions that are more consistent. However, non-uniqueness means an additional criterion is…
Real option valuation and equity markets
Many non-financial assets can be viewed as ‘real options’ linked to some underlying variable such as a commodity price. Here, Thomas Dawson and Jennifer Considine show that the stock price of a well-known electricity generating company is significantly…
Why be backward?
Originally developed as a tool for calibrating smile models, so-called forward methods can also be used to price options and derive Greeks. Here, Peter Carr and Ali Hirsa apply the technique to the pricing of continuously exercisable American-style put…
Dealing with discrete dividends
Over the past year, we have published several papers on the issue of options on stocks with discrete dividends. At least three distinct models are used by practitioners, involving trade-offs between accuracy and tractability. Here, Remco Bos, Alexander…
Mean-reverting smiles
Commodity markets such as crude oil exhibit mean reversion as well as option smiles. The authors construct a model suitable for pricing exotic options in these markets
Exotic spectra
Eigenfunction expansions can also be applied to finance. The method is particularly suited to barrier and Asian options, with convergence properties that compare favourably with Monte Carlo.
The need for hybrid models
In response to the above article, the authors argue that pure firm-value approaches to default prediction are fundamentally flawed.?
Black-Scholes goes hypergeometric
Option pricing models