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 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 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...

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...

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...

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...

Basket options are among the most popular products of the new generation of exotic options. This attraction is explained by the fact that they can efficiently and simultaneously hedge a wide variety of intrinsically different financial risks. They are flexible enough to include all the risks...

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...

Building Risk-Neutral Density (RND) from options data is one useful form of extracting market expectations about a financial variable. For a sample of IDI (Brazilian Interbank Deposit Rate Index) options from 1998 to 2009, this paper estimates the option-implied Risk-Neutral Densities for the...