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43 Cards in this Set
- Front
- Back
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Value of a Forward Position |
ST - [ FP / (1+RF)^T] |
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Forward Price of an Equity Security |
= (S - PVD) x (1+RF)^T |
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Value of a position on an equity fwd contract |
S - PVD - [FP / (1+RF)^T] |
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Value of a FWD on an equity index |
FP = S x e^(RF-DIV Yield)(T) |
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Value of long position on an equity index fwd |
S/e^DVY(T) - FP / e^RF(T) |
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Value of Currency FWD Contract |
= S/(1+Rfc)^T-t - F / (1+RDC)^T-t
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Continuous time forward contracts |
F = S x e^(Rdc-Rfc)(t) V = S / e^Rfc(T-t) - Ft / e^Rdc(T-t) |
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Important differences of FWDS and FUTs |
- Futures mtm each day
- Futures trade on an organized exchanged - FWDS customized, FUTS standardized - Clearinghouse in futures - Govt regulates futures |
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*Higher reinvestment rates and lower borrowing costs lead to a preference in futures when asset values are positive correlated* |
x |
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*If investors prefer to avoid MTM and int and asset values are negatively correlated, forward prices will be higher* |
x |
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Steps of cash and carry arbitrage |
At Initiation: 1)borrow $ for term of FUT contract 2) Buy asset at spot 3) Short the Futures At EXP: 1) Deliver asset and receive FUT price 2) Repay loan with interest |
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Convenience Yield |
Non-Monetary benefits from holding an asset in storage |
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Net Cost |
NC = Storage Costs - Convenience Yield FP = S x (1+RF)^T + FV(NC) Net Benefit = yield on asset + conv yield FP = S x (1+RF)^T - FV(NB) |
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Backwardation and Contango |
Backwardation is when future price is less than spot price |
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Future price of Treasury Bond FUT |
= ([Bond Price - PVC] x (1+RF)^T] / CF CF = Conversion Factor |
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Fiduciary Call |
Long euro call option Long pure discount bond |
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Protective Put |
Long euro put option Long stock position |
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Synthetic Call |
Buy stock Buy a euro put option Short the PV of x worth of pure discount riskless bonds |
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Synthetic Put Option |
Buy a euro put option
Short Stock Buy the discount bond |
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Synthetic Stock Position |
Buy a call option Short a put option buy the discount bond |
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Synthetic Bond |
Buy a put option buy a stock Short a call option |
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Put Call Parity |
Co = Po + So - [X / (1+RF)^T] Po = Co - So + [X / (1+RF)^T] |
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Risk neutral probability of an up move |
(1+RF-D) / U - D U = Size of up move D = Size of down move |
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Steps to calculate the value of a binomial option |
1) Calculate the payoff in both up and down moves 2) Calculate the EV of the option based on the probability of up and down moves 3) Discount the EV back to today |
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Delta |
(C1+ - C1-) / (S1+ - S1-) |
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Assumptions of Black Scholes Model |
- price of underlying follows lognormal dist
- continuous RF rate is constant and known - volatility of underlying asset is contstant and known - markets are frictionless - underlying has no cash flow - options are european |
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Five inputs to BSM |
- asset price - exercise price - asset price volatility - time to expiration - RF rate |
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Delta |
Relationship between asset price and option price positive for calls negative for puts |
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Vega |
Measures sensitivity of price to asset returns positive for both calls and puts |
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Rho |
Measures sensitivity in option prices to changes in RF rate - call option increases with RF rate - Put option decreases with RF rate |
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Theta |
Measures price sensitity to time - as time goes on, option value decays |
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Delta Hedged Portfolio |
Hedges long stock position with short call position # options = shares hedged / delta |
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Gamma |
measures the rate of change in delta |
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* cash flows reduce call values cash flows increase put values |
x |
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3 primary uses for swaptions |
1) lock in fixed rate 2) interest rate speculation 3) swap termination |
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Value of american options are higher for futures but the same for forwards |
x |
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common types of credit events in a CDS agreement |
bankruptcy failure to pay restructuring |
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factors that influence the price of a cds |
- probability of default - loss given default - coupon rate on swap |
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Loss given default |
Exp loss = Hazard rate x Loss given default |
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Upfront pmt by buyer |
PV(protection leg) - PV(Premium leg) |
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* Upfront premium = (CDS sprd - CDS coup) x duration CDS Sprd = upfront prem/duration x CDS coup |
x |
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Profit for buyer based on changes during the life of the CDS |
change in spread x duration x notional |
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x |
x |
