Topic 7: Option Market Mechanics and Properties of Stock Option Prices. Introduction. We now move from the study of futures and forwards to the study of options. A general outline for our options study is as follows: Market mechanics (Ch. 8 of Hull) Properties of Options (Ch. 9 of Hull)
VariableE. CallE. PutA. CallA. Put
Stock Price + - + -
Strike Price - + - +
Time to Exp. ? ? + +
Volatility + + + +
Risk-free rate + - + -
Dividends - + - +
c<= S and C<=S
p<=K and P<=K
PV(A) >= S0
which works to to be: c+Ke-r(T-t) >= S0, and rearranging
c>=S0 - Ke-r(T-t)
p+S >= Ke-r(T-t)
p>=Ke-r(T-t) - S
p>=max[Ke-r(T-t) - S, 0]
Sτ - K + Ke-r(T-τ)
while B is worth ST. Thus A is always worth at least as much as B, and sometimes more.
meaning that the American call option must be worth more than its intrinsic value.
C = intrinsic value + time value
What this argument really says is that time value for an American call is always positive.
A: One American put and one share
c>= S0 – D – Ke-rT
where D is the present value of the total dividends received during the life of the option, and
P>= D + Ke-rT-S0.
S0 – D – K <=C-P<=S0 – Ke-rT
c + Ke-rT = S0 +p,
p=c + Ke-rT - S0
p = 1.50 + 30e-0.0084(50/365) - 30.75 =0.7154
p = 1.60 + 30e-0.0084(50/365) - 30.75 =0.8155
Which is a lot closer to the put-call parity price. We still have the problem that the two trades occurred 14 minutes apart.