Many of the concepts in theoretical and empirical finance developed over thepast decades - including the classical portfolio theory, the Black-Scholes-Mertonoption pricing model and the RiskMetrics variance-covariance approach toValue at Risk (VaR) - rest upon the assumption that asset returns...

This chapter deals with the estimation of risk neutral distributions for pricing index options resulting from the hypothesis of the risk neutral valuation principle. After justifying this hypothesis, we shall focus on parametric estimation methods for the risk neutral density functions...

This paper proposes the use of analytical approximations to price an heterogeneous basket option combining commodity prices, foreign currencies and zero-coupon bonds. We examine the performance of three moment matching approximations: inverse gamma, Edgeworth expansion around the lognormal and...

This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics dVt = κt.(θt − Vt).dt λt.Vt.dBt. This non-affine model is much more realistic than classical affine models like the Heston stochastic volatility...

In the aftermath of the 2008 financial crisis, the need to consider more realistic risk models for derivative products has received renewed attention. We introduce a dynamic model for the pricing of European-style options with various attractive features such as a mixture of heavy-tails and...

We investigate the position of the Buchen-Kelly density in the family of entropy maximising densities from Neri & Schneider (2012) which all match European call option prices for a given maturity observed in the market. Using the Legendre transform which links the entropy function and the...

We obtain the maximum entropy distribution for an asset from call and digital option prices. A rigorous mathematical proof of its existence and exponential form is given, which can also be applied to legitimise a formal derivation by Buchen and Kelly (JFQA 31:143-159, 1996). We give a simple and...

Lognormal random variables appear naturally in many engineering disciplines, including wireless communications, reliability theory, and finance. So, too, does the sum of (correlated) lognormal random variables. Unfortunately, no closed form probability distribution exists for such a sum, and it...

Since its introduction in 2003, volatility indices such as the VIX based on the model-free implied volatility (MFIV) have become the industry standard for assessing equity market volatility. MFIV suffers from estimation bias which typically underestimates volatility during extreme market...

This paper examines the theoretically obtained prices with values based on temperature data in the Isle of Man and the UK. We have also seen that the simulated temperature trajectories do not appear to include entire seasons where the temperature remains cooler than normal. Anecdotally we have...