This is a short comment on Kung and Lee’s paper. In this note, we show that the formulae given in Kung and Lee(2009) for European call and put option under Merton’s model of the short rate are incorrect. We give the correct derivations making use of the ”change of numeraire” technique which is simpler and more standard. Key-words: Stochastic Interest rates, Change of Numeraire, Call option pric...

The duality principle in option pricing aims at simplifying valuation problems that depend on several variables by associating them to the corresponding dual option pricing problem. Here we analyze the duality principle for options that depend on several assets. The asset price processes are driven by general semimartingales, and the dual measures are constructed via an Esscher transformation. ...

In this paper, a new radial basis function (RBF) approach is developed for solving European option pricing model. Without any simplifications, a simple discretization pattern directly leads to a system Ax = b, moreover, employing a new variable shape parameter (VSP) strategy named binary shape parameter (BSP) strategy leads to more accurat results rather than constant shape parameter (CSP) stra...

American options are financial contracts that allow exercise at any time until expiration. While the pricing of standard American option contracts has been well researched, with a few exceptions no analytical solutions exist. Valuation of more involved American option contracts, which include multiple underlying assets or pathdependent payoff, is still to a high degree an uncharted area. Most n...

We consider series solutions for the location of the optimal exercise boundary of an American option close to expiry. By using Monte Carlo methods, we compute the expected value of an option if the holder uses the approximate location given by such a series as his exercise strategy, and compare this value to the actual value of the option. This gives an alternative method to evaluate approximat...

This paper investigates the characteristics of the higher moment risks of option returns, namely beta and coskewness. Under mild assumptions, the investors’ decreasing absolute risk aversion can result in a U-shaped pattern (a beta smile) for put option betas, though call option betas are always nondecreasing in the strike price. The coskewness for call options can be an inverted U-shape when t...

a r t i c l e i n f o This paper examines the relationship between option trading activity and stock market volatility. Although the option market is uniquely suited for trading on volatility information, there is little analysis on how trading activity in this market is linked to stock price volatility. The bulk of the discussion tends to focus on whether trading activity in the stock market i...

The behavior of the optimal exercise price American puts near expiry has been well studied under Black–Scholes model as a result series publications. However, stochastic volatility model, such Heston not reported at all. Adopting method matched asymptotic expansions, this paper addresses put options on dividend-paying underlying with expiry. Through our analyses, we are able to show that option...

This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined Black-Scholes closed form solution modified (MBS) partial differential equation using Crank-Nicolson finite difference method. These equations were approximated to obtain Call Put prices. The explicit price both options found accordingly. solutions c...