Option Pricing Model – An Imperfect Hedge

This paper is a rewrite of a former paper comparing the Louis Bachelier option pricing construct and that of Black Scholes Merton option pricing model, The present paper compares the construct and form of the Black-Scholes Merton (B-SM) and the Louis Bachelier option pricing models in terms of their contemporary markets and contracts, and the underlying pricing construct. To illustrate the comparison the Louis Bachelier model is adapted for features of modern traded option contracts by allowing for the premium's present value form, and incorporating the log-normal and continuous compound assumptions. This demonstrates the B-SM model approximation for the pdf at the boundary point using the differential in the cdf +/-the standard dispersal. This comparison concludes that the Black-Scholes Merton model, and its related precedents and antecedents, are thus approximations and derivative of the Louis Bachelier construct flowing from application of the Fourier heat equation. As part of the analysis the paper reviews critiques of the Bachelier construct in the financial literature; and similarly critiques the modelling and logical construct behind the Black-Scholes Merton model. In particular,

This paper builds on previous work on the Louis Bachelier option model and extends the concept to contract value and pricing rules. This enables certain implications to be defined in contingency and contract applications which are being developed at present.

Options are instruments which have the special property of limiting the downside risk, while not limiting the upside potential, thus their use in hedging. The share of the options market in the Indian capital market has increased to 64% in just over a decade. The trading turnover of options in the FY11 was Rs. 193,95,710 crore, and the trading volume generated by options market was almost two times that of the volume generated in the cash market and futures market put together. So trading and pricing of stock option have occupied an important place in the Indian derivatives market. Volatility is a critical factor influencing the option pricing; however, it is an extremely difficult factor to forecast. Hence the crucial problem lies with the accurate estimation of volatility. The estimated volatility can be used to determine future prices of the stock or the stock option. Empirical research has shown that using historical volatility in different option pricing models leads to pricing biases. The GARCH (1, 1) model can be a solution for this

2010

Options are instruments which have the special property of limiting the down side risk, while not limiting the upside potential, thus their use in hedging. The share of the options market in the Indian capital market has increase 64 % in just over a decade. This research paper emphasizes on the valuation of European call options by considering two industries comprising three companies respectively with 30 days of option expiry period from 2013 to 2015.Assessing the prices of two industries for particular period expiry with selected years for the study. It also explores relevance and accuracy of Black-Scholes Merton Option pricing model in predicting option prices. This research paper evaluates relative volatility of selected sample as the volatility is a significant factor influencing the option pricing; however, it is an awfully complex factor to forecast. Hence the crucial problem lies with the accurate estimation of volatility. The ballpark volatility can be used to establish future prices of the stock or the stock option. INTRODUCTION Derivative products originally materialized, as hedging devices against oscillation in commodity prices and commodity-linked derivatives remain the solitary form of such products for almost three hundred years. The financial derivatives came into spotlight in post-1970 period due to growing instability in the financial markets. However, since their emergence, these products have become very popular and by 1990s, they accounted for about two-thirds of total transactions in derivative products. In recent years, the market for financial derivatives has grown tremendously both in terms of variety of instruments available, their complexity and also turnover. In the class of equity derivatives, futures and options on stock indices have gained more popularity than on individual stocks, especially among institutional investors, who are major users of index-linked derivatives.

1997

This essay discusses the basic option pricing models - including the Binomial discrete model, the Black-Scholes continuous model, and their variants - and their mathematical derivations. It also provides an empirical evidence of options pricing and mispricing of the underlying securities that are traded in the markets. Moreover, some applications of option products are explored both as the market instruments and as the tailor-made contingent-claim contracts. Risk reduction, while enhancing returns through financial engineering, active assets allocation, and portfolios management, is possible and makes more sense if individual investors are aware of and familiar with the basic option pricing tools and their exotic applications. Sophisticated investors such as speculators, and hedgers, who are well-informed and have been equipped with these analytical capabilities, already squeezed extra returns from their investments in real and financial assets, let alone the institutional traders who seek arbitrage opportunities around the globe. Until all heterogeneous market participants are fluent with the language of derivative products and fine-tuned their expectations accordingly, the normative assumptions underlying modern finance theory will prove to be relevant in the real world.

The Financial Review, 2001

Dea Anjelinah, 2024

Tugas Akuntansi Syariah