You might find some inequality, but that's related to either an upcoming dividend or when there's a high stock lending fee... which would be the case in SVXY. But that's an interest rate matter and really, again, doesn't make a difference. Because both dividend and high lending fee cause the intrinsic value to drop, not the extrinsic. And by intrinsic value is meant the difference between strike price and underlying stock price including the interest rate component.
Hi JackRab, I started options trading only a few months ago, and I was not majored in finance or relative fields, but I am doing OK with high school math... Could you help me understand, analytically or quantitatively, why ITM strangle [+70C/+110P] is identical to OTM strangle [+70P/+110C]?
Part One:
Suppose we have strikes K1=70 & K2=110, underlying price S0=100, 60 days until maturity T=60, risk-free interest rate r, dividends present value D. Let C1 P1 C2 P2 be the price of 70C 70P 110C 110P respectively. And let us assume, for simplicity, that it is an European option. According to put-call parity on the two strikes, we have:
Eq1: C1 + D + K1 exp(-r T) = P1 + S0
Eq2: C2 + D + K2 exp(-r T) = P2 + S0
Subtracting the two yields:
Eq3: (C2 + P1) + (K2 - K1) exp(-r T) = (P2 + C1)
that is,
Eq4: Value[+70P/+110C] + 40exp(-60r) = Value[+70C/+110P]
I see the difference is 40exp(-60r), the interest rate component. Is the derivation above correct?
You said "the interest rate ... doesn't make a difference. Because both dividend and high lending fee cause the intrinsic value to drop, not the extrinsic. And by intrinsic value is meant the difference between strike price and underlying stock price including the interest rate component." I have some hard time understanding this part. Could you elaborate, analytically or quantitatively, on this a little bit?
Part Two:
Let's relax the assumption about European options; let it be an American option, with the possibility of early assignments. Put-call parity again:
Eq5: S0 - K1 <= C1 - P1 + D <= S0 - K1 exp(-r T)
Eq6: S0 - K2 <= C2 - P2 + D <= S0 - K2 exp(-r T)
Subtracting Eq6 from Eq5 yields:
Eq7: K2 exp(-r T) - K1 <= (C1 + P2) - (C2 + P1) <= K2 - K1 exp(-r T)
that is, Value[+70C/+110P] - Value[+70P/+110C] is bounded by range
[-K1 + K2 exp(-r T), K2 - K1 exp(-r T)]
or [-70 + 110exp(-60r), 110 - 70exp(-110r)]
If the above derivations correct? If so, is this range tight enough that you deem insignificant?
Sorry I am only savvy on high school math. Please correct me if anything is wrong...