Applications of Option-Pricing Theory: Twenty-Five Years Later

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Article American Economic Review June Theory ; Finance. A Framework for Understanding Financial Institutions. Merton and Robert T. Article Journal of Portfolio Management. Business and Environment Business History Entrepreneurship. Finance Globalization Health Care. Option pricing theory and applications General Management Marketing. Technology and Operations Management. About the Author Robert C. Thakor Financial institutions have both investors option pricing theory and applications customers.

Customers of a financial intermediary, in contrast, provide financing in exchange for a specific set of services, and do not want the fulfillment of these services to be contingent on the credit risk of the intermediary, even when they are not small, uninformed agents lacking in sophistication. Option pricing theory and applications paper develops a framework that defines the roles of customers and investors in intermediaries, and uses the framework to provide an economic foundation for the aversion option pricing theory and applications intermediary credit risk on the part of its customers.

It further explores the implications of this customer-investor nexus for option pricing theory and applications host of issues related to how contracts between financial intermediaries and their customers are structured and how risks are shared between them, as well as the consequences of unexpected deviations from the ex ante optimal contractual arrangement.

We show that the optimality of insulating the customer from the credit risk of the intermediary explains various contractual arrangements, institutions, and regulatory practices observed in practice. Moreover, customers and investors are often intertwined in practice, and so this intertwining provides insights into the adoption of "too-big-to-fail" policies and bailouts by regulators in general.

Finally, the approach taken here shows that financial crises may be a consequence of observed but unexpected deviations from the ex ante optimal risk-sharing arrangement between financial intermediaries and their customers.

Merton Corporate America began to really take notice of the looming retirement crisis in the wake of the dot-com crash, when companies in major industries went bankrupt in large part because of their inability to meet their pension obligations. The result was an acceleration of America's shift away from employer-sponsored pension plans toward defined-contribution DC plans—epitomized by the ubiquitous k —which transfer the investment risk from the company to the employee.

With that transfer has come option pricing theory and applications dangerous shift in investment focus, argues Nobel Laureate Robert C. Traditional pension plans were conceived and managed to provide members with a guaranteed income. And because that objective filtered right through the scheme, members thought of their benefits in those terms. Ask a member what her pension is worth and she'll reply with an income figure: Most DC schemes, however, are designed and managed as investment accounts with the goal of accumulating the largest possible pot of savings.

Communication with savers is framed entirely in terms of assets and returns. Ask a saver what his k is worth and you'll hear a cash amount and perhaps a lament to the value lost in the financial crisis.

The trouble is that investment value and asset volatility are simply the wrong measures if your goal is to secure a particular future income. In this article, Merton explains a liability-driven investment strategy whose aim is to improve the probability of achieving a desired retirement income rather than to maximize the capital value of the savings.

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The share price follows a random walk and that the possible share prices are based on a normal distribution. One of the limitations of the Black-Scholes formula is that it assumes that the shares will not pay dividends before the option expires. In fact, if no dividends are payable before the option expiry date, the American call option will be worth the same as a European call option. Simply deduct the present value of dividends to be paid before the expiry of the option from the current share price.

The following information relates to a call option: Black-Scholes model is a model for determining the price of a call option. The market value of a call option can be calculated as: The formula will be given in the examination paper. You need to be aware only of the variables which it includes, to be able to plug in the numbers. Using the Black-Scholes model to value put options The put call parity equation is on the examination formula sheet: Value the corresponding call option using the Black-Scholes model.

Then calculate the value the put option using the put call parity equation. Underlying assumptions and limitations The model assumes that: The options are European calls.

There are no transaction costs or taxes. The investor can borrow at the risk free rate. The future share price volatility can be estimated by observing past share price volatility. No dividends are payable before the option expiry date. Application to American call options One of the limitations of the Black-Scholes formula is that it assumes that the shares will not pay dividends before the option expires.

If this holds true then the model can also be used to value American call options. Illustration The following information relates to a call option: The dividend-adjusted share price for Black-Scholes option pricing model can be calculated as: Application of option pricing theory in investment decisions.