Forward payoff
Long: profit per unit = S(T) - F(0,T)
Short: profit per unit = F(0,T) - S(T)
Total = profit per unit x quantity
Any forward or futures profit question. Decide your side first: buying forward makes you the long, selling forward the short.
- S(T)
- Spot price of the asset at delivery
- F(0,T)
- Forward price agreed at the start, for delivery at T
Default-risk exposure on a forward
Exposure at time t = PV{ |F(0,T) - F(t,T)| }, 0 < t < T
When a question asks who has the incentive to default and how much is at stake. The defaulting party is the one for whom the contract is a liability.
- F(t,T)
- Today's forward price for delivery on the original delivery date T
- PV
- Present value, discounting from T back to t at the rate for that tenor
Margin account, one day at a time
Contract value = lot size x number of lots x price
Initial margin = margin % x contract value
MTM (long) = (today - yesterday) x quantity
MTM (short) = (yesterday - today) x quantity
Equity = previous equity + MTM + variation margin
Call fires when equity < maintenance margin
Variation margin = initial margin - equity
Every mark-to-market table. Work one row at a time and never skip the equity line, because the call is tested on equity, not on the price.
- quantity
- Units controlled: lot size times number of lots
- maintenance margin
- Minimum equity that must be kept in the account
- variation margin
- Top-up called for, sized to restore equity to the initial margin
Price move that triggers the first call
Cushion = initial margin - maintenance margin
Adverse move allowed per unit = cushion / quantity
When asked how far the price can go before a margin call. Convert the equity cushion into a price move using the number of units, never the number of lots.
- cushion
- Equity available above the maintenance level