fm part 2
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Author:
contango
ID:
283401
Filename:
fm part 2
Updated:
2014-10-13 20:03:06
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part
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nothin
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Macaulay Duration
denominator is price P(i)
Modified duration
represents sensitivity of price change in the interest rate
Convexity
Duration of a portfolio
= present value weighted average of the durations of the individual components.
i.e., Durations are weighted by price
Conditions for Redington immunization
1.
2.
or duration assets = duration liabilities
3.
or convexity assets > convexity liabilities
Conditions for full immunization with one cash outflow
1.
2.
3. There is one cash inflow before and one after the outflow
payoff and profit with purchased call option
payoff
profit
K is the strike price
S_T is the spot price out T years
C is the premium for the option
payoff and profit with purchased put option
payoff
profit
K is the strike price
S_T is the spot price out T years
C is the premium for the option
payoff for long forward
Protective put
Long position in the asset + purchased put
Profit equivalent to purchased call
Insuring a short position
Short position in the asset + purchased call
Profit equivalent to purchased put
Covered call
Long position in the asset + written call
Profit equivalent to written put
Covered put
Short position in the asset + written put
Profit equivalent to written call
Put-call parity
Call(K,T) - Put(K,T) = PV(F
_{0,T}
- K)
Recall how this relates to synthetic forwards vs long forwards.
Note PV(F) = S
_{0}
Cash and carry
Short forward + purchased stock (with borrowed money)
Can be used for arbitrage and market-making
_{}
Four ways to buy a stock
Outright purchase:
Receive stock at time 0
Pay S
_{0}
at time 0
Borrow to pay for stock:
Receive stock at time 0
Pay S
_{0}
e
^{rT}
at time T
Prepaid forward:
Receive stock at time T
Pay at time 0
= S
_{0}
- PV(dividends)
Forward contract: