Option pricing
Sponsored statement: The problems with generally used interpolation spaces
In a world increasingly focused on effective enterprise-level risk management, there are notable discrepancies in volatility management techniques. Murex proposes a cross-asset interpolation space with potentially significant risk management impacts
The inflation pricing conundrum
Fear of a spike in consumer prices has created greater demand for inflation protection from a variety of participants. This has increased the need for inflation pricing and analytics tools – but it is not as simple as tweaking existing models used for…
Expanded smiles
Implementing models with stochastic as well as deterministic local volatility can be challenging. Here, Jesper Andreasen and Brian Huge describe an expansion approach for such models that avoids the high-dimensional partial differential equations usually…
Interview with Vladimir Piterbarg
Vladimir Piterbarg talks about his new article published in the Cutting Edge section of Risk magazine
Funding beyond discounting: collateral agreements and derivatives pricing
Standard theory assumes traders can lend and borrow at a risk-free rate, ignoring the intricacies of the repo and collateralisation markets. Here, Vladimir Piterbarg shows that these force adjustments to discounting, forward prices and implied…
Smile dynamics IV
Lorenzo Bergomi addresses the relationship between the smile that stochastic volatility models produce and the dynamics they generate for implied volatilities. He introduces a new quantity, the skew stickiness ratio (SSR), and shows how, at order one in…
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