Efficient likelihood estimation of Heston model for novel climate-related financial contracts valuation

Abstract

We propose novel Bitcoin-denominated derivatives contracts on carbon bonds. We consider a futures contract on carbon bonds where its price is expressed in terms of bitcoins. Then, we put forward options on a futures contract of the former type. Governments can use such contracts to hedge climate change and influence the prices of carbon bonds and cryptocurrencies. We show how these derivatives transfer volatility to the bitcoin market without a negative effect in the carbon bonds market. Since the aforementioned options are not yet traded in the market, we price them by assuming that the underlying is driven by the well-known Heston model, where the model parameters are estimated by a novel method based on Shannon wavelets. Heston model belongs to the class of stochastic volatility (SV) models. The discrete observations from the SV model can be seen as a state-space model, that is, a stochastic model in discrete-time which contains two sets of equations, the state equation and the observation equation. While the first describes the transition of a latent process in time, the second shows how an observer measures the latent process at each time period. We infer the properties of the latent variable by means of a filtering algorithm, and we estimate the parameters of the model via maximum likelihood. The evaluation of the likelihood function is a time-consuming task that involves updating and prediction steps of the state variable, leading to the computation of complicated integrals. We calculate these integrals by means of an integration method based on Shannon wavelets, and compare the root mean square error (RMSE) of the estimation with state-of-the-art methods. The results show that the RSME is dramatically reduced in a short CPU time with the use of wavelets.