Since the pioneering paper of Black and Scholes was published in 1973, enormous research effort has been spent on finding a multi-asset variant of their closed-form option pricing formula. In this paper, we generalize the Kirk [Managing Energy Price Risk, 1995] approximate formula for pricing a...

Since the launch of 50 ETF index option in February 2015, its trading volume keeps increasing year by year. This reflects the strong potential of the Chinese option market. As there were few English research on the 50 ETF option, I was very interested in applying the Black-Scholes (BS) and...

In this paper, we investigate the behavior of the bitcoin (BTC) price through the vanilla options available on the market. We calibrate a series of Markov models on the option surface. In particular, we consider the Black-Scholes model, Laplace model, five Variance Gamma related models and the...

We analyze the implied volatility smile of a lognormal distribution on a 3 – month Danske bank call option contract using the option delta. There is significant time variation in the implied volatility smile and the traditional Black – Scholes model can not explain this deviation. The Black...

This paper introduces an option pricing algorithm based on non-orthogonal series expansion methods. More precisely, Gabor frame decomposition is used to split the risk neutral option pricing formula into the sum of two inner products that can be evaluated efficiently by means of Parseval's...