Hi David,
In the Derivatives II screencast I have a doubt in the Put call parity formula explanation. You said that “ on the left hand side....Ke^-rt is the face value of a bond we have purchased.......” my question is how does the value remain at 10 when we increase the price of the bond to 13 or decrease it to 7......

also if that (10) is the termination value, the value will be 10 only if the disc rate used and interest prevailing are equal (as per my understanding) but nothing has been mentioned on that front...so the basic question is how does the equality hold good?

Thanks a ton.

Regards,
Animesh

Hi Aminesh,

The scenarios only change the stock price, not the bond (the “bond” here is just another way of saying we borrow cash equal to the future value of the strike price). This may relate to your second part, but here put-call parity says:

call + $10 = put + stock

e.g., if stock goes up to $13, then
3 + 10 = 0 + 13

e.g., if stock goes down to $7, then
0 + $10 = 3 + 7

so the bond is merely another way of saying “we borrow the future value of the exercise price.”
Importantly, put-call parity applies only if the STRIKE price is the same for both the call and the put,
so the Strike Price = K and we borrow K*EXP[(-r)T]. Precisely so we can have cash in the exact amount of the strike in the future.

“the value will be 10 only if the disc rate used and interest prevailing are equal”
Correct, but in this case, the RISKLESS rate indicates we borrow at the riskfree rate b/c we want no uncertainty that the future amount will be (K). That is, we are borrowing a Treasury and holding to maturity. This is the beginning of the risk neutral valuation idea: the use of a riskless rate here indicates the future $10 cash is certain (no variation) and helps to make the payoffs certain.

I think i see your point; if we buy a risky bond and do not hold to maturity, the interest rate (market risk) may produce a value different than $10. But here the idea is we are taking out a risk free loan with maturity equal to the holding period (no market risk)

David