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Unformatted text preview: previous section we begin with the One period case
There are two possible outcomes for the stock called heads (H ) and tails (T ).
⇠⇠ S1 (H ) = S0 u
⇠⇠
⇠⇠
S 0 XX
XX
XX
S1 (T ) = S0 d We assume that there is an interest rate r, which means that $1 at time 0 is
the same as $(1 + r) at time 1. For the model to be sensible, we need
0 < d < 1 + r < u. (6.1) Consider now an option that pays o↵ V1 (H ) or V1 (T ) at time 1. This could
be a call option (S1 K )+ , a put (K S1 )+ , or something more exotic, so we
will consider the general case. To ﬁnd the “no arbitrage price” of this option
we suppose we have V0 in cash and 0 shares of the stock at time 0, and want
to pick these to match the option price exactly:
✓
◆
1
1
V0 + 0
S1 (H ) S0 =
V1 (H )
(6.2)
1+r
1+r
✓
◆
1
1
V0 + 0
S1 (T ) S0 =
V1 (T )
(6.3)
1+r
1+r
Notice that here we have to discount money at time 1 (i.e., divide it by 1 + r)
to make it comparable to dollars at time 0.
To ﬁnd the values of V0 and 0 we deﬁne t...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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