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 afutures contract on carbon bonds where its price is expressed in terms of bitcoins. Then, we putforward options on a futures contract of the former type. Governments can use such contracts tohedge climate change and influence the prices of carbon bonds and cryptocurrencies. We showhow these derivatives transfer volatility to the bitcoin market without a negative effect in thecarbon bonds market. Since the aforementioned options are not yet traded in the market, weprice them by assuming that the underlying is driven by the well-known Heston model, wherethe model parameters are estimated by a novel method based on Shannon wavelets. Hestonmodel belongs to the class of stochastic volatility (SV) models. The discrete observations fromthe SV model can be seen as a state-space model, that is, a stochastic model in discrete-timewhich contains two sets of equations, the state equation and the observation equation. Whilethe first describes the transition of a latent process in time, the second shows how an observermeasures the latent process at each time period. We infer the properties of the latent variableby means of a filtering algorithm, and we estimate the parameters of the model via maximumlikelihood. The evaluation of the likelihood function is a time-consuming task that involvesupdating and prediction steps of the state variable, leading to the computation of complicatedintegrals. We calculate these integrals by means of an integration method based on Shannonwavelets, and compare the root mean square error (RMSE) of the estimation with state-of-the-artmethods. The results show that the RSME is dramatically reduced in a short CPU time with theuse of wavelets.