2 - Pricing of futures and forwards Flashcards
What are the two fundamental assumptions when seeking to price futures and forwards?
- No arbitrage
- Replication
No arbitrage meaning ?
Markets are efficient and arbitrage cannot persist
Replication meaning?
The payoffs of the derivative product (in this
case the future or the forward) are
determined by price movements in the
underlying assets.
The derivative can be “replicated” by using
the underlying assets
Time notation:
0
T
0 - current date
T - Maturity Date of the Forward (yrs)
Price notation:
S0
ST
F
S0 - Current price of the underlying asset
ST - The price of the underlying asset at time = T
Is the maturity price of the forward
F - Delivery price of a forward
PV(F)=PV(S)
PV(F) - Forward strategy
This is, at time = 0, the present value of the single payment under the futures contract upon delivery of the asset
PV(S) - Replication strategy
Involves:
1. Holding benefits e.g. dividends or coupons
2. Holding costs e.g. storage or insurance cists
Formula for replication strategy which includes Net holding costs?
PV(S)=S0 + M
S0 - spot price at time T = 0
M - Net holding costs (replication strategy)
= PV(holding costs) - PV(holding benefits)
Formula for for forward strategy which includes Net holding costs?
PV(F) = S0 + M
What are the principle assumptions when using pricing futures and forwards?
- No transaction costs
- No restrictions on short sales
- The rates of interest are the same for borrowing and lending
PV(F)>S0 +M meaning?
The futures is over-valued and the spot is undervalued
Therefore, to arbitrage the position the arbitrageur must short the futures and long the spot
PV(F)<S0 + M meaning?
The futures is under-valued and the spot is over-valued
Therefore, to arbitrage the position the arbitrageur must long the futures and short the spot
What does short the futures and long the spot mean?
Enter a position to sell asset in the future.
Borrow money for the period of the futures instrument
Buy x unit(s) of asset on the Spot Mkt
Repay borrowings when the futures settles
What does long the futures and short the spot mean ?
Enter a position to buy asset in the future. Sell x unit(s) of asset on the Spot Mkt
Invest proceeds for the period of the futures instrument
Buy back x unit(s) of asset on the Spot Mkt
what does the model PV(F)<S0 + M assume?
Assumes that you hold assets, have spare available and want it back or can borrow and then return assets
What are the pricing model limitations?
.Delivery Options
.Margining (Daily Marking to Market)
.Transaction costs
.Restrictions on Short Sales
(e.g. catastrophe futures where the underlying is not traded & electricity where the cost to hold it is
prohibitively expensive)
.Different rates of interest for borrowing and lending
(incl. the default-free or risk-free rate of interest)
What is the hedging strategy for this model:
PV(F) NOT= Smid + M
- Take advantage of the price mismatch (using the SPOT market)
- Seek to trade out of the position
- Hold the original position
What are the practical issues when hedging?
- There may be an asset and delivery mismatch
- Margining for futures contracts would have to be considered
What are asset mismatches?
The assets underlying the original contract may not be available
What are delivery mismatches?
It may be impossible to absolutely match the delivery criteria of the original contract in the current market
What are hedges?
A way of protecting oneself against financial loss or other adverse circumstances
What are short hedges?
An attempt to manage risk using an agreement to sell an asset/assets at a point in the future
What are long hedges?
An attempt to manage risk using an agreement to buy an asset/assets at
a point in the future
State which are fixed and variable:
The Original Forward Price
The Present Value of the Forward
The Spot Market Price
Fixed
Variable
Variable
