Options: Lesson 1

One of my favorite topics in finance is that of options. I've mentioned options in a few previous posts, and I would like to dedicate a few posts to the mechanics of options and option pricing. Coincidentally, this is also the same material that I'm studying for my next RL actuarial exam, exam MFE (Modeling: Financial Economics).

Options are power. There are no markets in Second Life that trade options. Some are afraid investors will use them without understanding them. Others are swamped fixing other bugs so that the thought of including derivatives is nearly impossible at present. Regardless, options exist in real life, and they're useful in real life. Whether they ever exist in SL, these lessons will teach you about what options are, how they operate, and how to price them (at least basically). I'll be using some mathematics for this, and the lessons will build on each other.

For our purposes, we will concentrate on options on an underlying stock. However, you should know that options also exist on futures, currencies, indexes, and even other options. Each of these brings a new caveat to the stage, but for my sanity I'm going to stick to cash and stocks.

There are two broad types of options. I'm going to go over them very slowly:

A call option gives the owner the right, but not the obligation, to buy an underlying stock at a specified strike price (K) by time T.

A put option gives the owner the right, but not the obligation, to sell an underlying stock at a specified strike price (K) by time T.

Read those two sentences again. And again. One more time.

Also know that I'm describing American options in the definitions above. If they were European options, they would have ended with "at time T" instead of "by time T." Some of the pricing models will only value European options, but I'll make sure to warn you ahead of time.

If the price of the underlying stock is denoted as S, then the payoff of the call option is

Call Payoff = Max{0,S-K}

This is because if the stock price (S) is below the strike price (K), then you simply choose not to exercise the option (why buy the stock at K when it's selling at S?). If S > K, though, you can buy at K and then sell at S, netting S-K for yourself. Similarly, the payoff for a put option is

Put Payoff = Max{0,K-S}

If the stock price (S) is below the strike price (K), then you can buy the stock at S and sell it at K, netting you K-S. If S > K, then you would prefer to sell at S, and so it is not advantageous to exercise your put option (and thus the value is zero).

Wikipedia has some nice graphs of a call payoff and put payoff, which I encourage you to look at.

That's it for lesson 1. Subsequent lessons will get into the pricing, and then the all-important parity equation and how that functions. More math coming, I promise!

Please, if you have questions, ASK! This material can be very confusing, even for advanced traders. I'm probably going to speed up, not slow down, in the next lesson, so get questions out of the way now. If you're too shy to post them here (even anonymously), then email me at guardian.market@gmail.com.