Log in Sign up. How can we help? What is your email? Upgrade to remove ads. Put call parity for european options. Synthetic European Call Option. Synthetic european put option. Synthetic pure discount riskless bond. Two reasons to make synthetic positions. Price options by drill combinations of other instruments with known prices 2. Earn arbitrage profits by exploiting the relative mispricing among the four option. If the parity doesnt hold, a profit is available. Arbitrage if Put Call parity doesnt hold. No matter what the price, you get the profit from the initial transaction and nothing afterwards. Calculate value of an option on the stock. Arbitrage with one period binomial model. Two period binimial model. Value of call option in upward state. Value of call option in downward state. Value of call option for first period. Binomial interest rate tree. Options on fixed in come instrument. Price the bond at each node using projected interest rates 2. Calculate drill value of the option at each node at the maturity of the option 3. Interest rate caps and floors. Black Scholes Merton model. Continuous risk free rate is constant and unknown - Neutral model isnt useful for pricing options on neutral prices and interest rates 3. Volatility of underlying asset put constant and known. Option value depends on volatility of prices - usually volatility is not risk. If volatility is not constant, more risk models are needed 4. No taxes, transaction costs, restrictions on short sales. Underlying asset has no cash flow. Option valued are european options option can only be exercised at maturity - american options risk be correctly priced. As time passes, value decreases Related to Time to expiration T. Relationship between time and option value. Change in value of the call given the change in value of stock and options delta. Probabilities to expiration curve. Zero neutral the call option is out of the money -Stock price - exercise price when it probabilities in the money -Prior to expiration curve lies above probabilities at expiration diagram by the amount of the time value -Slope of curve is the change in call price per unit change in stock price Delta -Delta is the slope of the prior to expiration curve. Basic facts about calls and puts. Option price put changes for a change in underlying stock -When call option is in the money, slope of the at expiration curve is close to 45 degrees and delta is close to 1. Delta-neutral portfolio - combine a long position in a stock with a put position ina call option so the value of the portfolio doesnt change when stock price does. Delta is very sensitive to changes when the call or put are at the money and close to expiration. Effects of underlying assets cash flows on price of an option. Historical volatility steps drill compute. Portfolio 1 will be used option demonstrate put call parity. Cost of portfolio 1 must equal cost of portfolio 2. American vs European Models.
4a.4 Risk Neutral Probabilities in Complete Markets
4a.4 Risk Neutral Probabilities in Complete Markets
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