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...

Abstract. Equity warrants are instruments that bestow upon the holder of the instrument the right to buy a particular stock at a predetermined price within a stipulated time frame. However, to gain this right, the buyer of such warrants usually needs to make an upfront payment to the warrants...

We seek to estimate a portfolio of option prices in an entirely data driven way, at any future time, for trading and risk management purposes in a model independent way. We do not know the model driving the dynamics of the actual stock prices, but only observe discretely their evolution in the...

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...

We present a unified, market-complete model that integrates both Bachelier and Black- Scholes-Merton frameworks for asset pricing. The model allows for the study, within a unified framework, of asset pricing in a natural world that experiences the possibility of negative security prices or...

In this short paper, we study the asymptotics for the price of call options for very large strikes and put options for very small strikes. The stock price is assumed to follow the Black-Scholes models. We analyze European, Asian, American, Parisian and perpetual options and conclude that the...

Purpose: The aim of the paper is to investigate the Black and Scholes model by providing an updated framework of the international literature on the topic, within the field of real option. The purpose of the research is to identify the relevant literature between 1999 and 2015, together with the...