Option to Ride

I had a couple of interviews today.. which meant that I had to rely on the subway to get around. My aunt or uncle would usually drop me off at Taman Paramount(TP) where I'd take the train to KL. On the way back, I would stop at TP if I can hitch a ride from my kind relatives; otherwise, I would alight 2 stops earlier at Taman Jaya(TJ) where there is always a ready supply of taxis(mostof the time!).

A trip to TJ from KL costs $2.00 while TP costs $2.10. so... That's a 10 cent difference if i bought the ticket from KL. However a ticket from TJ to TP would cost about $1.50. I wont know if i will get a ride home from the relatives until I call them as I'm reaching the station. Taxi ride home costs an average $5.80.

This data is summarised on the pay OUT diagram on your left...(all should be negative!) where ride means a ride from my relatives and taxi means... you get the drift.. Well, you might notice that I put the price of taxi as $0.00, well because in the valuation of this option(SURPRISE! THIS IS AN OPTION!) the cost of the taxi would be a future 'sunk cost' because I will have to get home one way or the other.

Investopedia.com says: Options are financial instruments that convey the right, but not the obligation, to engage in a future transaction on some underlying security, or in a futures contract

The underlying transaction here would be to not pay $1.50 to get to TP.

ASSUMING, a risk neutral world(i.e everything has equal chance of occurence), the inherent value of not paying 10 cents more at KL would be $0.75 ( 1.50*5o%+0*50%). Which means that we WOULD be willing to pay anything under $0.75 to hedge against paying $1.50 to go from TJ to TP. Thus with a $0.10 initial outlay for an option valued at $0.75, the future risk managing director in me shouted out BUY recommendations.

So i did...

However.. I ended up taking the cab anyhows... ...