Finance 2 - Lecture 4 summary
Finance 2 (FEB13001)
Erasmus Universiteit Rotterdam
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Lecture 4 Properties of stock options and parity 1. If the stock price increases, the probability that spot P strike P is high, thus buyer of the call option is better off and is willing to pay more for the option. The buyer of the put option is worse off and thus, is willing to pay less. 2. If the strike price increases, the probability that strike P spot P is high, the buyer of the call option is worse off and is willing to pay less. The buyer of the put option is better off and thus, is willing to pay more. 3. Because stock P is volatile and both put and call option buyers would like to hedge themselves, the option prices are higher with increased volatility. 4. When there are dividends, buyer of the call option does not receive them or even in some instances need to pay them back, is willing to pay less for the option. The reverse is true for the buyer of the put option. 5. Discount rate is higher, then, the Future P increases, which can be considered as a spot P. As a result, the probability that spot P strike P is high, thus, buyer of the call option is better off and is willing to pay more for the option. The buyer of the put option is worse off and thus, is willing to pay less. When the call (put) price is lower than the lower bound for the call price arbitrage opportunity. The investment at is 0, but the profit at time T 0. Properties of option prices Call price cannot be exceed the stock price and be lower than the PV of the difference between the forward price and the strike price (otherwise, there is an arbitrage opportunity). Put price cannot be exceed the strike price and be lower than the PV of the difference between the strike price and the forward price. parity Synthetic forward (buy the call and sell the put) must be priced consistently with actual forwards. Putcall parity is a principle that defines the relationship between the price of European put options and European call options of the same class, that is, with the same underlying asset, strike price and expiration date. parity states that simultaneously holding a short European put and long European call of the same class will deliver the same return as holding one forward contract on the same underlying asset, with the same expiration and a forward price equal to the strike price. If the prices of the put and call options diverge so that this relationship does not hold, an arbitrage opportunity exists, meaning that sophisticated traders can earn a theoretically profit. F(0,T) forward prepaid forward price. If underlying asset is a stock that pays dividends, the prepaid forward price is S therefore: Index options are with continuous dividends. The true reason why call options are more expensive than the put ones is the time value of money. Parity provides a cookbook for the synthetic creation of options, stocks and Synthetic stock To match the CF for an outright purchase of the stock, in addition to buying the call and selling the put, we have to lend the PV of dividends and strike price. Synthetic Buy stock, sell call, buy put (conversion). Short the stock, buy a call and sell a put (reverse conversion). We have created a position that costs and that pays at expiration. Synthetic call Buy a stock, buy put, borrow PV of strike and div Synthetic put sell stock, buy call, lend PV of strike and div Comparing options wrt style, maturity and strike Since an American option can be exercised at any time whereas a European option can only be exercised at expiration, an American option must always be at least as valuable as an otherwise identical European option:
Finance 2 - Lecture 4 summary
Vak: Finance 2 (FEB13001)
Universiteit: Erasmus Universiteit Rotterdam
