FM(Derivative_Markets衍生品市场)知识点总结

1 Name Graph Description Payoff Profit Comments Long Forward Commitment to purchase commodity at some point in the future at a pre- specified price ST - F ST – F  No premium  Asset price contingency: Always  Maximum Loss: -F  Maximum Gain: Unlimited Short Forward See above Commitment to sell commodity at some point in the future at a pre- specified price F - ST F - ST  No premium  Asset price contingency: Always  Maximum Loss: Unlimited  Maximum Gain: F Long Call (Purchased Call) Right, but not obligation, to buy a commodity at some future date Max[0, ST – K] Max[0, ST – K] – FV(PC)  Premium paid  Asset price contingency: ST>K  Maximum Loss: - FV(PC)  Maximum Gain: Unlimited  COB: Call is an Option to Buy  “Call me up”: Call purchaser benefits if price of underlying asset rises Short Call (Written Call) Commitment to sell a commodity at some future date if the purchaser exercises the option - Max[0, ST – K] -Max[0, ST – K] + FV(PC)  Premium received  Asset price contingency: ST>K  Maximum Loss: FV(PC)  Maximum Gain: FV(PC) Long Put (Purchased Put) Right, but not obligation, to sell a commodity at some future date Max[0, K - ST] Max[0, K - ST] - FV(PP)  Premium paid  Asset price contingency: K>ST  Maximum Loss: - FV(PP)  Maximum Gain: K - FV(PP)  POS: Put is an Option to Sell  “Put me down”: Put purchaser benefits if price of underlying asset falls  Short with respect to underlying asset but long with respect to derivative 2 Short Put (Written Put) Commitment to buy a commodity at some future date if the purchaser exercises the option -Max[0, K - ST] -Max[0, K - ST] + FV(PP)  Premium received  Asset price contingency: K>ST  Maximum Loss: -K + FV(PP)  Maximum Gain: FV(PP)  Long with respect to underlying asset but short with respect to derivative Floor Long Position in Asset + Purchased Put  Used to insure a long position against price decreases  Profit graph is identical to that of a purchased call  Payoff graphs can be made identical by adding a zero-coupon bond to the purchased call Cap Short Position in Asset + Purchased Call  Used to insure a short position against price increases  Profit graph is identical to that of a purchased put  Payoff graphs can be made identical by adding a zero-coupon bond to the purchased put Covered call writing Long Position in Asset + Sell a Call Option Long Index Payoff + {-max[0, ST – K] + FV(PC)}  Graph similar to that of a written put Covered put writing Short Position in Asset + Write a Put Option - Long Index Payoff + {-max[0, K - ST] + FV(PP)}  Graph similar to that of a written call 3 Synthetic Forward Purchase Call Option + Write Put Option with SAME Strike Price and Expiration Date {max[0, ST – K] – FV(PC)} + {-max[0, K - ST] + FV(PP)}  Mimics long forward position, but involves premiums and uses “strike price” rather than “forward price”  Put-call parity: Call(K,T) – Put(K,T) = PV(F0,T – K) Bull Spread Purchase Call Option with Strike Price K1 and Sell Call Option with Strike Price K2, where K2>K1 OR Purchase Put Option with Strike Price K1 and Sell Put Option with Strike Price K2, where K2>K1 {max[0, ST – K1] – FV(PC1)} + {-max[0, ST – K2] + FV(PC2)}  Investor speculates that stock price will rise  Although investor gives up a portion of his profit on the purchased call, this is offset by the premium received for selling the call Bear Spread Sell Call Option with Strike Price K1 and Purchase Call Option with Strike Price K2, where K2>K1 OR Sell Put Option with Strike Price K1 and Purchase Put Option with Strike Price K2, where K2>K1 {-max[0, ST – K1] + FV(PC1)} + {max[0, ST – K2] - FV(PC2)}  Investor speculates that stock price will fall  Graph is reflection of that of a bull spread about the horizontal axis Box Spread Bull Call Spread Bear Put Spread Synthetic Long Forward Buy Call at K1 Sell Put at K1 Synthetic Short Forward Sell Call at K2 Buy Put at K2 Consists of 4 Options and creates a Synthetic Long Forward at one price and a synthetic short forward at a different price  Guarantees cash flow into the future  Purely a means of borrowing or lending money  Costly in terms of premiums but has no stock price risk Ratio Spread Buy m calls at strike price K1 and – sell n calls at strike price K2 OR Buy m puts at strike price K1 and - sell n puts at strike price K2  Enables spreads with 0 premium  Useful for paylater strategies 4 Purchased Collar Buy at-the-money Put Option with strike price K1 + Sell out-of- the-money Call Option with strike price K2, where K2>K1  Collar width: K2 - K1 Written Collar Sell at-the-money Put Option with strike price K1 + Buy out-of- the-money Call Option with strike price K2, where K2>K1 Collared Stock Buy index + Buy at-the-money K1- strike put option + sell out-of-the- money K2 strike call option, where K2>K1  Purchased Put insures the index  Written Call reduces cost of insurance Zero-cost collar Buy at-the-money Put + Sell out- of-the-money Call with the same premium  For any given stock, there is an infinite number of zero-cost collars  If you try to insure against all losses on the stock (including interest), then a zero-cost collar will have zero width Straddle Buy a Call + Buy a Put with the same strike price, expiration time, and underlying asset  This is a bet that volatility is really greater than the market assessment of volatility, as reflected in option prices  High premium since it involves purchasing two options  Guaranteed payoff as long as ST is different than K  Profit = |ST – K| – FV(PC) – FV(PP) 5 Strangle Buy an out-of-the-money Call + Buy an out-of-the money Put with the same expiration time and underlying asset  Reduces high premium cost of straddles  Reduces maximum loss but also reduces maximum profit Written Straddle Sell a Call + Sell a Put with the same strike price, expiration time, and underlying asset  Bet that volatility is lower than the market’s assessment Butterfly Spread Sell a K2-strike Call + Sell a K2- strike Put AND Buy out-of-the-money K3-strike Put AND Buy out-of-the-money K1-strike Call K1< K2< K3  Combination of a written straddle and insurance against extreme negative outcomes  Out of the Money Put insures against extreme price decreases  Out of the Money Call insures against extreme price increases Asymmetric Butterfly Spread λ = K3 - K2 K3 – K1 Buy λ K1-strike calls Buy (1 – λ) K3-strike calls K2 = λK1 + (1 – λ)K3 K1< K2< K3 Cash-and- carry Buy Underlying Asset + Short the Offsetting Forward Contract  No Risk  Payoff = ST + (F0,T – ST) = F0,T  Cost of carry: r – δ Cash-and- carry arbitrage Buy Underlying Asset + Sell it forward  Can be created if a forward price F0,T is available such that F0,T > S0e (r – δ)T 6 Reverse cash- and-carry Cash Flow at t=0 Cash Flow at t=T Short-tailed position in stock, receiving S0e -δT S0e -δT -ST Lent S0e -δT -S0e -δT S0e (r – δ)T Long Forward 0 ST – F0,T Total 0 S0e (r – δ)T – F0,T Short Underlying Asset + Long the Offsetting Forward Contract  Payoff = -ST + (ST - F0,T) = -F0,T Reverse cash- and-carry arbitrage  Can be created if a forward price F0,T is available such that F0,T < S0e (r – δ)T If… THEN If Volatility ↑ If Unsure about Direction of Volatility Change If Volatility ↓ Price ↓ Buy puts Sell underlying asset Sell calls Unsure about Direction of Price Change Buy straddle No action Write straddle Price↑ Buy calls Buy underlying asset Sell Puts Reasons to hedge Reasons NOT to hedge 1. Taxes Transaction costs (commissions, bid-ask spread) 2. Bankruptcy and distress costs Cost-benefit analysis may require costly expertise 3. Costly external financing Must monitor transactions to prevent unauthorized trading 4. Increase debt capacity (amount a firm can borrow) Tax and accounting consequences of transactions may complicate reporting 5. Managerial risk aversion 6. Nonfinancial risk management Method of purchasing stock Pay at time Receive security at time Payment At time Outright Purchase 0 0 S0 t=0 Fully-leveraged purchase T 0 S0e rT t=0 Prepaid Forward Contract 0 T S0e -δT t=T Forward Contract T T S0e (r - δ)T t=T r = Continuously-compounded interest rate δ = Annualized daily compounded dividend yield rate α = Annualized Dividend Yield: (1 ÷ T) × ln(F0,T ÷ S0) 7 Pricing Prepaid Forward and Forward Contracts: Prepaid Forward Contract FP0,T Forward Contract F0,T No Dividends S0 S0e rT Discrete Dividends S0 - ∑PV0,t(Dt) S0e rT - ∑er(T – t)×Dt Continuous Dividends S0e -δT S0e (r - δ)T Initial Premium Initial Premium = Price = FP0,T Initial Premium = 0 Price = F0,T = FV(F P 0,T) Forwards Futures Obligation to buy or sell underlying asset at specified price on expiration date Same Contracts tailored to the needs of each party Contracts are standardized (in terms of expiration dates, size, etc.) Not “marked to market”; settlement made on expiration date only “Marked to market” and settled daily Relatively illiquid Traded over-the-counter and handled by dealers/brokers Liquid Exchange-traded and marked to market Risk that one party will not fulfill obligation to buy or sell (credit risk) Marked to market and daily settlement minimize credit risk Price limits are not applicable Complicated price limits