Option Premium - The amount an option costs per share. Since option contracts are for 100 shares, the amount quoted is multiplied by 100.
Intrinsic Value - For a call option; the current market price of the stock minus the option strike price. For a put option; the current strike price of the option minus the current market price of the stock. If the answer is zero or negative, the option has no current intrinsic value. That is the same as saying the option is at-the-money or out-of-the-money. Intrinsic value does not change with time. Intrinsic value is a measure of the in-the-moneyness of the option.
Time Value - The current option premium minus the intrinsic value. The Time Value of an option is dependent on the probability that the option will expire in-the-money. The longer the time until expiry, the greater the probability the option will expire in-the-money. Time Value of an option decays, that is, as you approach the expiration date of the option, the time value approaches zero. At expiration date, you are left with the Intrinsic Value. Either the option is in the money, or it expires worthless.
The value of an option is calculated using the Black-Scholes equation for European options or other similar equations for American Options. The equation uses the mean price of the stock, the standard deviation of its price changes during the measurement period and the risk free rate available to the purchaser. These equations allow you to calculate the Time Value of the option since it is a function of the log normal returns from the stock.
The value of an option is mathematically derived and is not dependent on your hopes and dreams of making it BIG - sorry Bob.
I'll answer some more of Bob's questions about options in another post.
Thanks again Bob for the questions.
Need Help on A Binomial Pricing Model:
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Well, I am looking to use a standard binomial tree model to simulate probable movements in the underlying (S&P 100). The problem I am running into arises from the fact that these options are American-style and Cash-settled. The risk of early assignment causes the boxes with deeper options in them to trade at a premium. Also, the cheaper puts have a serious volatility skew. Standard modelling methods simply do not apply. Should I try to write these variables into my equation, or add premium, depending on circumstance? Considering the circumstances and nature of volatility and time decay, I suspect that some kind of smoothing might be required.
I've tried several pricing models and none do the job adequately for my analytical needs. I know that there are proprietary models out there that are quite accurate, and I would like to mimic their procedures whereever possible.
As far as using the stochastic formula inside a spreadsheet, the functions (in Excel, of course) to get the high over a range is max[l1:l2] and to get the low over a range is min[l1:l2]. I don't know about Lotus 1-2-3 tho ... but it should be something similar.
As of yet, the only thing I could come up with (and you probably are already aware of) is either the Black-Scholes or the Cox-Ross-Rubenstein models. Both are quite similar, with the CRR model requiring you to work backwards to assess the value to the option at EACH branch of the tree.
1. You must figure out the
individual price volatility
for each strike (good luck!)
2. And/or you must re-write your
model to give more volatility
to the wings.
Let me tell you, this is a MAJOR task!
The proprietary models out there which are quite accurate are also VERY expensive (thousands of dollars). A friend of mine's technical trading group spent an entire year developing their software to do this very thing. I asked her for the equations and she just laughed at me. (I laughed too!)
Posted by: Bob Hansell | February 14, 2006 8:23 PM | Permalink to Comment