Friday, December 21, 2007
Some thoughts on option
Just checked: the underlying has almost picked up but the call option price remained less than halved. I hope I learned a hard lesson over "time value" of options. Some of the basic things I want to keep in mind: never hold an option if not for hedging purposes, never buy an option when volatility is perceived high, and never just bet with gut feeling.
Wednesday, December 19, 2007
Wednesday, December 12, 2007
Betting
So I took a hard beat yesterday because I bet on the wrong side regarding Fed decision (with a long position in index call). In the mean time, I started to think of a very basic yet interesting problem: let us say participants in the market are betting on a single event of two outcomes, and they know where one asset price would be for either outcome of this event. What would the asset price be right before the event?
For simplicity, let us say there will be two outcomes: H & L. For H, the price of the asset would go up to H, for L it goes to L. Assume betters can both long & short their positions. Assume they are risk-neutral. Confidence over H outcome is denoted by x, and the pdf of betters (weighed with their capitals, of course) with x confidence is p(x). We have \Integrate p(x) dx = 1 as the constraint. The market price of the asset P right before the event, is determined by the following equation:
in which, x0=(P-L)/(H-L), because whoever has a confidence over x0 would long the asset while others short it, and long positions should be equal to short ones.
PS: Thinking again, it might not be this simple. The final price could in some degree depend on the path - I shall do a simulation some day. It is an easy job. Keep bid-ask spread in mind.
For simplicity, let us say there will be two outcomes: H & L. For H, the price of the asset would go up to H, for L it goes to L. Assume betters can both long & short their positions. Assume they are risk-neutral. Confidence over H outcome is denoted by x, and the pdf of betters (weighed with their capitals, of course) with x confidence is p(x). We have \Integrate p(x) dx = 1 as the constraint. The market price of the asset P right before the event, is determined by the following equation:
\Integrate [0,x0] p(x) = 1/2,
in which, x0=(P-L)/(H-L), because whoever has a confidence over x0 would long the asset while others short it, and long positions should be equal to short ones.
PS: Thinking again, it might not be this simple. The final price could in some degree depend on the path - I shall do a simulation some day. It is an easy job. Keep bid-ask spread in mind.
