How Can You Evaluate the "Right" Price of Your Option?

TK All-Star posted on 06/13/11 at 09:49 AM



Mark Wolfinger responds to a real-world trader's question on Black-Scholes and options pricing 

TK trader isg123 posted an interesting question to the forums recently:

 

I recently read the Big Short. In it, a market participant claims that the Black-Scholes model assumes a normal price distribution for underlying stocks and therefore would not be accurate for special situation stocks or very unpopular trades such as buying an SPY Dec 13 900 Put.

If this is true how can I get a feel for potential profit, assuming my thesis is correct and SPY drops to 500 before Dec 13?  (TK's P&L Calculator is based on Black-Scholes)

 

 

Hello isg123,

 

Knowledge is powerful and it’s important to understand what you are trading and how options are valued. If you dislike Black-Scholes, you can always find other options calculators by using Google. However, let's talk about the main theme of your question:

 

First, a clarification: the ETF SPY is trading in the 130s, so I'll assume your forecast refers to the index SPX. If you believe that SPX will trade at 500 by the end of 2013, there is no need to be concerned with how much you can make. If this theoretical actually occurs, that’d be a profitable (and lucky) scenario for you. But you need to determine how likely this scenario seems in reality, not just how lucky you feel.

 

Although theoretical option value is always important, it becomes a lot less important when the options you own are very deep in the money (ITM). All you must do for the strategy you outlined above is be able to calculate the intrinsic value for put options. No calculator is needed for that.

 

On the other hand, if you want to buy the Dec 13 500 puts at a price near $10, then you will want to estimate the option’s value at given SPX levels. I urge you NOT to buy those options. How would you feel to see SPX decrease to 600 – you would be right in anticipating the huge move, but if it doesn't happen until late 2013, your puts could become worthless. Give yourself some room in case the market does not tumble quite that far, that fast. It’s a rookie mistake to load up on options that are too far out-of-the-money. I'd steer clear of doing that.

  

Here’s one example. Let’s say you buy some SPX Dec 13 600 puts for about $1,800 each. (Don't forget to factor in commissions on top of that - at TradeKing this trade would cost you $5.50 in commissions for a one-lot.) If SPX is trading at 500, then the intrinsic value of the option would be $100 (subtract the index price from the strike price to get the intrinsic value). There may be some residual time value, depending on how much time remains before expiration. But the important part is that intrinsic value. That’s $10,000, and its value increases by $100 for every point that SPX is below 500.

 

The obvious problem is which options to buy. Going all the way out to Dec 2013 makes the options expensive. You probably cannot afford to, or would want to, buy expensive puts, even if each one would be ITM by at least 200 points and be worth at least $20,000. Do you want to buy the 600 puts at $1,800?

 

You may want to go for more leverage, using less cash – even if it limits profits. One possibility is to buy the SPX Dec 13 500/600 P spread at a price near $8 ($800 cash).  Each of these can eventually be worth $10,000 if your market outlook becomes reality. If that happens, the spread would offer a better return on your investment.

 

The bottom line for right now: recognize that you do not really need to know the expected value of these options to the last dollar. And one major reason for that is you can assume a significant rise in implied volatility if SPX declines all the way to 500. Unless you make a fairly accurate guess as to when your prediction comes true and a reasonable estimate for the IV that will be in place at that time, your calculator is going to be very far away from reality anyhow. Time to expiration, coupled with IV, play a huge role in determining the value of an option. 


Thanks for this thought-provoking question.

  

 

Regards,
Mark Wolfinger
Partner, ExpiringMonthly.com and Founder, MDWOptions.com
TradeKing All-Star Commentator

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Posted by TK All-Star on 06/13/11 at 09:49 AM

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