American Basket Option Pricing Formulas in Uncertain Environment

American basket option is a contract containing multiple underlying assets, and its payoff is correlated with average prices or weighted average prices of these assets on or before the expiration date. The type of option entitles a holder the right to trade at the strike price within a specified date, and this right can be waived. Therefore, there is a certain price to be paid for acquiring this right, which produces the problem of option pricing. A lot of literature shows blackthat basket option price is usually cheaper than option portfolios on individual underlying assets. Based on this advantage, basket option blackbecomes popular among investors. Consequently, this paper predominantly explores four types of American basket option pricing in uncertain financial environment. Specifically they are American arithmetic basket call option, American arithmetic basket put option, American geometric basket call option and American geometric basket put option. Assuming that these stocks prices follow corresponding uncertain differential equations, we derive corresponding option pricing formulas. Some numerical examples are taken to illustrate the feasibility of pricing formulas. Simultaneously, this paper discusses the relationship between option price and some parameters.

Numerical Valuation of American Basket Options via Partial Differential Complementarity Problems

We study the principal component analysis based approach introduced by Reisinger and Wittum (2007) and the comonotonic approach considered by Hanbali and Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour.

Evaluation of Equity-linked structured products and pricing

Based on a unique data set, this research paper examines the pricing of equity-linked structured products in the market. The following section of this paper look at examining a few popular products available in the market, describing their key characteristics, and identifying one such product which will be examined closely for the purposes of determining if the issuing institution has priced the same fairly. The daily closing prices of a large variety of structured products are compared to theoretical values derived from the prices of options traded on the Eurex (European Exchange). This research paper also provides a brief background on the pricing of equity-linked structured products (‘products’) and issues around valuation of these products and look in detail fair pricing of the zero-coupon bond and the basket option. Comparing this with the market price of the instrument I could draw conclusions based on how close the real market price of the instrument is with the recomputed price.

A General Accurate Approximation for Pricing and Hedging Basket Options with Exact Moment Matching

This article provides a new methodology for pricing and hedging basket options. The authors approximate the basket by using the shifted log-normal distribution with the polynomial expansion, which can match exactly any required m moments of the basket, to give quasi-analytical formulas for the prices and hedging parameters of basket options. Numerical simulations show that the methodology provides superior results for basket option prices and hedging parameters. This methodology works well not only for regular baskets but also for negative-weight baskets and negative-value baskets. Compared with the best available methods, the authors’ methodology appears to perform better.