Unformatted text preview: α)S0 u + (1 − q )(1 + α)S0 d )
1+r Which we could write as
1+α
S0 =
(qS0 u + (1 − q )S0 d )
1+r This is our old equation but with B (1 + α) instead of B
Old formula works with B (1 + α) replacing B :
q= 1
B (1+α) −d u−d Note: Hull also uses ”continous compounded dividend yield”. The
analog of:
1
e −rt vs
(1 + r )t Option on a currency Suppose that the current exchange rate is 1.6 USD/GBP. Next
year, the rate will either go up to 1.7 or down to 1.5. How much
would it cost to buy a call option on GBP struck at 1.6
USD/GBP? Suppose that rUS = 3% and rUK = 5%.
Here instead of a stock, the underlying is a currency. If you hold
the currency, you are entitled to a dividend through interest
payments. Let S0 be the current exchange rate (the price of the
foreign currency). Option on a currency (continued) If I spend 1.6USD to buy one unit of GBP, I will have 1.05 units of
GBP at the end of the year. So my total CF at the end of the year
will be 1.05 S1 where S1 is the future exchange rat...
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 Spring '13
 Options, Mathematical finance, CF

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