Option pricing
Heston model: shifting on the volatility surface
Fitting the implied volatility surface is generally a complicated affair. Here, Claudio Pacati, Roberto Renò and Manola Santilli propose a simple extension of the Heston model that allows fast and arbitrage-free interpolation of the volatility surface…
Cutting edge: Incorporating forex volatility into commodity spread option pricing
In this article, Joseph Yechong Chen extends Kirk’s formula to spread option pricing when forex is a stochastic factor and is multiplied to one leg in the payoff formula. The article illustrates the importance of forex risk factors and the need to…
Smile transformation for price prediction
Options prices are driven by supply and demand in the market while simultaneously being bound by no-arbitrage restrictions. This makes it difficult to create models for their prediction. Petros Dellaportas and Aleksandar Mijatović use a simple time…
Time for a timer
Timer options are derivatives that expire when the underlying’s realised variance hits a certain level, adding another layer of complexity that is usually tackled with computationally costly numerical methods. Minqiang Li and Fabio Mercurio show how…
Hedge backtesting for model validation
Derivatives pricing and expected exposure models must be backtested as a basic regulatory requirement. But what does this mean exactly, and how can it be used to reserve against model risk? Lee Jackson introduces a general backtesting framework for…
Smile in the low moments
Skew and curvature of volatility smiles are not only difficult to estimate, but also poorly reproduced by most smile expansions. Jean-Philippe Bouchaud, Lorenzo De Leo, Vincent Vargas and Stefano Ciliberti propose an expansion that effectively captures…
Rational shapes of local volatility
The asymptotic behaviour of local volatility surfaces for low and high strikes – the so-called wings – is important in option pricing and risk management. Stefano De Marco, Peter Friz and Stefan Gerhold show certain models allow for the derivation of…
Physics versus finance: Science strikes back
After almost two decades in which Wall Street was a magnet for quantitative analysts, science is rediscovering its pull, says Stephen Blyth
Risk reaches 25-year anniversary
In celebration of our 25th anniversary this year, Risk re-publishes a landmark article by Fischer Black, offering a critique of the Black-Scholes model
Technology: Cloud on the horizon?
Banks need more processing power, and cloud computing offers it. But there are a host of practical issues – from loss of control to regulatory scepticism – that could hold up its adoption. Clive Davidson reports
Sponsored feature: Royal Bank of Scotland
Insurers frequently find themselves on the wrong side of the distortions but, by using efficient hedging techniques, they can identify opportunities to turn these distortions to their advantage.
Quanto adjustments in the presence of stochastic volatility
It is well known that the quanto adjustment in the drift of the underlying has a significant impact on the prices of quanto options. Alexander Giese points out that an additional quanto adjustment in the underlying’s volatility needs to be considered in…
Stochastic volatility’s orderly smiles
Lorenzo Bergomi and Julien Guyon derive an expansion of the volatility surface of general stochastic volatility models at second order in volatility of volatility that is accurate for a wide range of strikes. They characterise the shape of stochastic…
Sponsored statement: Ito33
Local volatility was, for a long time, seen as being a universal panacea. However, cracks appeared and we have been forced to look elsewhere for a new framework. Philippe Henrotte, co-founder, partner and head of financial theory and research at Ito33,…
Downgrade termination costs
Ratings-based (RB) additional termination event (ATE) clauses in International Swaps and Derivatives Association agreements can have a significant impact on the valuation of derivatives portfolios when rating events occur. Fabio Mercurio, Roberto Caccia…
Need for speed: banks explore FPGAs for portfolio modelling
It can take hours for traditional bank systems to run portfolio risk models. That’s too slow for some banks, which are now exploring unwieldy – but quick – field-programmable gate arrays. By Clive Davidson
Cutting Edge introduction: requiem for a probabilist
The already challenging task of calibrating stochastic volatility models becomes even more complex when rates are random too. But an efficient Monte Carlo approach can be found – by using an esoteric, but neglected, stochastic calculus. Laurie Carver…
Perturbed Gaussian copula: introducing the skew effect in co-dependence
Gaussian copula models are often used in the industry when single-asset information is quoted but little is known about their joint relation. These models may arise from correlated stochastic Brownian processes with deterministic volatility and…