Financial Options Pricing History. Today we will learn How do Investors Price Options?
These classes are all based on the book Trading and Pricing Financial Derivatives, available on Amazon at this link. amzn.to/2WIoAL0
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Up to now we have looked at how options work and how they can be combined. We have mentioned options premium and how it is made up of time value and intrinsic value. In this video we will look at a few of the most common methods for pricing options. The value of options depends on a number of different variables in addition to the value of the underlying asset. They are complex to value and there are many pricing models in use. All models essentially incorporate the concepts of rational pricing, intrinsic value, time value, and put-call parity.
In this video we will give you some insight as to how different variables affect option prices, and we hope to show you that while these methods are extremely useful, they are quite fallible, and can only give you an indication of fair value that is extremely dependent on the inputs into the formulas. The old “garbage in, garbage out” adage is particularly applicable to derivatives valuation-and most of financial mathematics. The formulas we will look at are only as good as the numbers that are put into them and often rely on a number of assumptions that do not always hold up in live securities market trading. They all rely on an estimate of volatility, and on an assumed distribution, that cannot be known in advance.
In general, standard option valuation models depend on the following factors:
• The current market price of the underlying security
• The strike price of the option
• The cost of holding a position in the underlying security, including interest and dividends
• The time to expiration together with any restrictions on when exercise may occur
• An estimate of the future volatility of the underlying security’s price over the life of the option.
Options, or option-like contracts have been around for hundreds of years. Only in the 1970s was a formal pricing model introduced..
Options contracts are very similar to insurance contracts, and so most of the ideas used to price them came from the insurance business. As early as 1350 in Palermo, insurance contracts were common for casualty and credit risks relating to shipping. The two kinds of insurance were often being written separately. A popular contract was a conditional sale (similar to a put option) where the insurer agreed to purchase ship or cargo if it failed to arrive.
Louis Bachelier (1870-1946) was a French mathematician credited with being the first person to model the stochastic process now called Brownian motion, which was part of his PhD thesis “The Theory of Speculation,” published in 1900. His thesis, which discussed the use of Brownian motion to evaluate stock options, is historically the first paper to use advanced mathematics in the study of finance. Thus, Bachelier is considered a pioneer in the study of financial mathematics and stochastic processes. Bachelier’s thesis was not well received because it attempted to apply mathematics to an unfamiliar area for mathematicians.
We know the fair value of an options contract at expiration based upon the payoff diagrams, and we know that options are worth more than their value at expiration before the expiration date due to time value.
Option value = Intrinsic value + Time value
Before mathematical formulas existed for pricing options we knew that the fair value of options was higher than intrinsic value, as there was still time for the underlying to move in your favor, but not how much higher the price should be. Option prices, like all market prices, were just a capital weighted average of every market participant’s best guess as to what fair value should be. Should an investor feel that option prices were too high, they could simply sell some options, and this would push the price down to where other investors felt they were too cheap and thus were willing to buy them.
Tune in tomorrow for Patricks Video on the Binomial Tree approach for pricing options.
15 фев 2019
