A question about Black&Scholes Option pricing ?

Why are you trying to learn something that directly or indirectly caused the greatest hedge fund collaspe of recent times which almost caused the collaspe of our whole economy?

you know what I mean?

Ok, there are a couple of issues here. The first one is, you have 100 shares of stock that you're looking to "hedge" by selling calls. This is not a hedge, it's an income producing strategy used for stocks that don't seem to have a lot of upside potential (going sideways) that you'd like to earn a little extra income on called writing (selling) calls. Each option contract that you sell represents the obligation of selling 100 shares of the underlying stock at the strike price on expiration.

So in the case you outline above, you say you're looking to write 31 calls, this represents 3100 shares of stock, which means you'd be naked on 3,000 shares or $300,000. I don't know too many brokers who are going to allow you to do naked call writing like that. The reason for this is because your liability is unlimited to the upside potential of the stock. Let's say your scenario doesn't work out and the stock closes at 120 on expiration. You now have to buy 3000 shares at 120 and sell them at 100, that's a huge loss. So that's your real downside, the upside potential of the stock.

Also, your math is wrong. 31 calls sold for $7 is $21,700 in premium (because each call = 100 shares, 3100 x $7).

You would only do something like this if A. your broker allowed you to have this much liability (unlikely unless you're a multimillionaire) and B. if there was a high probablity of the stock going down $7 or more in 15 days. If that were the case, then the volatility (delta) of the stock would be much higher, and so would the option value.

Basically, you are on the hook for selling 3000 shares of stock for $100, so your "downside risk" is really unlimited because the price of the stock (hypothetically) can go to infinity.

If you'd like to fool around with the formula and try some real calculations, try the link below which brings you to the CBOE options calculator. While there, you should check out the booklet, "Characteristics and Risks of Standardized Options" Good luck - happy trading!

There are several things wrong with your problem. The main one is that you have not calculated the hedge ratio properly. The hedge ratio comes from the Delta. Since you do not specify a volatility, I can't calculate the right delta. However, if volatility is 60%, then the delta is about 0.73 -- not 0.31. A volatility of 40% gives a delta of about 0.88. Either of these would cut down on that loss you mention. The hedge ratio is N(d1) -- not d1 (where N() is the standard normal cumulative distribution).

The Delta tells you the approximate change in value of the option for a small change in the underlying value. So, for a ten cent drop in price, a call option with a delta of 0.73 should lose about 7.3 cents. The price of an option is not a linear function of the underlying price -- so it does not accurately project the change in option price for a large change in price of the underlying (like $7.00). In theory, you should be continuously changing the size of your position if you want to hedge properly. Transaction costs prohibit you from doing this effectively.

Hey buddy, I think all this Black Scholes stuff is junk, I think it is meant to give you an understanding of how the option works, but I dont believe you can really hope to make money by applying it, pratically. There are computer programs out there that solve this type of problem for you, why would you want to understand the mechanics of the math.