Call and Put Price Bounds
Tags: #Financial #EconomicsEquation
$$(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \le c(S_{t},K,t,T) \le F^{P}_{t,T}(S) \\ (Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \le p(S_{t},K,t,T) \le Ke^{-r(T-t)} \\ c(S_{t},K,t,T) \le C(S_{t},K,t,T) \le S_{t} \\ p(S_{t},K,t,T) \le P(S_{t},K,t,T) \le K$$Latex Code
(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \le c(S_{t},K,t,T) \le F^{P}_{t,T}(S) \\
(Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \le p(S_{t},K,t,T) \le Ke^{-r(T-t)} \\ c(S_{t},K,t,T) \le C(S_{t},K,t,T) \le S_{t} \\
p(S_{t},K,t,T) \le P(S_{t},K,t,T) \le K
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Introduction
Equation
Latex Code
(F^{P}_{t,T}(S) - Ke^{-r(T-t)})_{+} \le c(S_{t},K,t,T) \le F^{P}_{t,T}(S) \\
(Ke^{-r(T-t)} - F^{P}_{t,T}(S))_{+} \le p(S_{t},K,t,T) \le Ke^{-r(T-t)} \\
c(S_{t},K,t,T) \le C(S_{t},K,t,T) \le S_{t} \\
p(S_{t},K,t,T) \le P(S_{t},K,t,T) \le K
Explanation
Latex code for the Calls and Puts Arbitrage. The following equations give the bounds on the prices of European calls and puts. Note that the lower bounds are no less than zero. We can also compare the prices of European and American options using the following inequalities.
: European Call Option Price
: European Put Option Price
: American Call Option Price
: American Put Option Price
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Comments
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Wishing I could just snap my fingers and pass this test.
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