Forward contracts If F>Ser(rt, you can earn an arbitrage profit by taking the following positions at t (cash is not required) borrow s dollars at rate r Buy 1 unit of asset Take a short position in the forward contract Charles cao 16
16 Charles Cao Forward Contracts ◼ If F > St e r(T-t) , you can earn an arbitrage profit by taking the following positions at t (cash is not required): ◼ Borrow St dollars at rate r ◼ Buy 1 unit of asset ◼ Take a short position in the forward contract
Forward contracts At time Sold the asset for ST Pay back the loan -ser(Tt) Realize a profit F-ster(tt>0 Charles cao
17 Charles Cao Forward Contracts ◼ At time T: ◼ Sold the asset for ST ◼ Pay back the loan, -St e r(T-t) ◼ Realize a profit, F – St e r(T-t) > 0
Forward Contracts: Example 1 a forward contract is written on a stock The maturity of the contract is 6 months. The stock price is $50 today and the risk-free rate is 10% per year Recall F=Ser(T-t Charles cao
18 Charles Cao Forward Contracts: Example 1 ◼ A forward contract is written on a stock. The maturity of the contract is 6 months. The stock price is $50 today and the risk-free rate is 10% per year ◼ Recall r(T t) t F S e − =
Forward Contracts: Example 1 Tt=0.5 year =0.1 S=$50 Thus the forward price is F=50e0105=S52.56 Charles cao 19
19 Charles Cao Forward Contracts: Example 1 T-t = 0.5 year r = 0.1 St = $50 Thus, the forward price is: 50 $52.56 0.1 0.5 = = F e
Forward Contracts: Example 2 a forward contract is written on a discount bond. The maturity of the contract is 4 months. The bond price is $950 today and the risk-free rate is 8% per year Recall F=St e(l Charles cao 20
20 Charles Cao Forward Contracts: Example 2 ◼ A forward contract is written on a discount bond. The maturity of the contract is 4 months. The bond price is $950 today and the risk-free rate is 8% per year ◼ Recall r(T t) t F S e − =