Forecasting volatility is important to financial asset pricing because a more accurate forecast will allow for a more accurate model to price financial assets. Currently the VIX is used as a measure of volatility in the market as a whole, but a major issue with this is that it is calculated based on manually traded options on the S&P 500. Another method of forecasting volatility is that of solv...

What is an Option? An option gives the holder the right, but not the obligation to either buy or sell some stated underlying asset at an agreed exercise price ('strike price'), either before or at some fixed date. In a legal sense an option can be categorised as a 'contingent claim' contract. The seller of an option (also known as a 'writer') grants the purchaser this right (option) in return f...

We consider a popular problem in finance, option pricing, through the lens of an online learning game between Nature and an Investor. In the Black-Scholes option pricing model from 1973, the Investor can continuously hedge the risk of an option by trading the underlying asset, assuming that the asset’s price fluctuates according to Geometric Brownian Motion (GBM). We consider a worst-case model...

We investigate qualitative and quantitative behavior of a solution to the problem of pricing American style of perpetual put options. We assume the option price is a solution to a stationary generalized Black-Scholes equation in which the volatility may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We de...

In this work, we extend the applicability of regret minimization to pricing financial instruments, following the work of [10]. More specifically, we consider pricing a type of exotic option called a fixed-strike lookback call option. A fixed-strike lookback call option has a known expiration time, at which the option holder has the right to receive the difference between the maximal price of a ...

An e cient algorithm is developed to price European options in the presence of proportional transaction costs, using the optimal portfolio framework of Davis (1997). A fair option price is determined by requiring that an in nitesimal diversion of funds into the purchase or sale of options has a neutral e ect on achievable utility. This results in a general option pricing formula, in which optio...

Internet Auction is a one of the most successful e-Commerce markets. Recently, it has been reported that the trades having buyout options are increasing. A " buyout option " is available in many Internet auction sites. When a seller uses a buyout option, a " buyout price (buy price) " of the good is set by the seller. If a buyer submits a bid equal to the buyout price, the auction immediately e...

We propose the use of the Kramers-Moyal expansion in the analysis of third-order noise. In particular, we show how the approach can be applied in the theoretical study of option valuation. Despite Pawula's theorem, which states that a truncated model may exhibit poor statistical properties, we show that for a third-order Kramers-Moyal truncation model of an option's and its underlier's price, i...

In this paper, we examine an exchange economy with a financial market composed of three assets: a share of a stock, an European call option written on the stock, and a riskless bond. The financial market is assumed to be incomplete and the option is not a redundant asset. In such a case the construction of a riskless hedge-portfolio to valuate the option is unfeasible and therefore the pricing ...

We solve the following three optimal stopping problems for different kinds of options, based on the Black–Scholes model of stock fluctuations. (i) The perpetual lookback American option for the running maximum of the stock price during the life of the option. This problem is more difficult than the closely related one for the Russian option, and we show that for a class of utility functions the...