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6 Options II

3 if the value of portfolio a at in all states i 1m

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Unformatted text preview: is lower and P is higher for options with bigger K. 2. Principles of Portfolio Replication: a) These variations on the “Law of One Price” are used heavily in the arbitrage arguments underlying most option pricing theory. Consider portfolios A and B and future states of the world i = 1…m: • Portfolio A costs A0 to obtain today and will be worth {A(i)T, i = 1…m} at time T • Portfolio B costs B0 to obtain today and will be worth {B(i)T, i = 1…m} at time T b) From these, we can deduce the following principles: #1 If the distribution of values {A(i)T} ≡ {B(i)T}, then the current values A0 = B0, or else an arbitrage opportunity exists. Ec 174 OPTIONS II p. 2 of 18 #2 If all values in the distribution in {A(i)T} ≥ values in the distribution in {B(i)T}, then A0 ≥ B0, or else an arbitrage opportunity exists. #3 If the value of portfolio A = AT in all states i = 1…m, then A0 = ATe−rT with certainty, or else an arbitrage opportunity exists. Table 2 3. Factors Affecting Stock Option Value: [Table 2] Increase in Factor C P Current Stock Price St + − a) The effect of stock price (St) and strike price (K) on Strike Price K − + intrinsic value. Time to maturity T + + 1) Immediate call payoff is St – K if exercised. For both Stock Price Volatility σ + + American and European options: Expected Dividends D − + • Given K, Ct should rise as St rises. • Given St, Ct should be lower for higher K. 2) Immediate put option payoff is K – St. For both American and European options: • Given K, Pt should fall as St rises. • Given St, Pt should be higher for higher K. b) The effect of time to maturity (T) on time value. 1) American options can be exercised at any time up thru date T. The farther away is T, the more possible for asset price movements to push the option “into the money” at some point, and the more freedom the investor has to profit by choosing the right time for exercise. Therefore, for American options, cet. par.: • Both Ct and Pt should be hig...
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