Anyone else not get to grips with this? It sounds the same as a Butterfly spread strategy. Both are long bear spread and long bull spread. Could someone explain a Box Spread Strategy

Quoting from notes, so not guarantee 100% is correctness. It has been a while. Boxed spread: combination of long bull spread + long bear spread. Constant payoff for all situations --> used only for arbitrage. Butterfly Spreads: buy 2 calls and sell 2 calls at MIDDLE price to finance the original calls = buy a bull spread and short another Bull at cheaper price to finance. Used to bet a static situation. Pay off: peak around current price.

Correct, the Box Spread earns the RISK FREE RATE if there are no pricing discrepancies. If there are then a box spread can risklessly gain from the discrepancies. In a butterfly spread, the peak payoff is the strike of the middle calls.

you are partly correct in that a box spread is long bull spread and a long bear spread such that total positions can be summarized as: long bull spread: LONG a call with X(L) and SHORT a call with X(H) long bear spread: LONG a call with X(H) and SHORT a call with X(L) but for a butterfly spread, the positions are: long a call with X(L) long a call with X(H) short 2 calls with X(M) where X(M) is somewhere in between high and low exercise price. since X(M) is not equal to X(H), the two strategies are not similar in that respect. chedges Wrote: ------------------------------------------------------- > Anyone else not get to grips with this? It sounds > the same as a Butterfly spread strategy. Both are > long bear spread and long bull spread. > > Could someone explain a Box Spread Strategy

chedges Wrote: ------------------------------------------------------- > Anyone else not get to grips with this? It sounds > the same as a Butterfly spread strategy. Both are > long bear spread and long bull spread. > > Could someone explain a Box Spread Strategy As a matter of fact, the intention of the two strategies are quite different including the legs. For butterfly, for simplicity, let’s assume this discussion is abt CALL Butterrfly (either all legs are only calls, or only puts), with made-up concrete number: +1 x 5%ITM Call (wing) - eg. E-mini S&P M0 1140C -2 x ATM Call (body) - eg. E-mini S&P M0 1200C +1 x 5%OTM Call (wing) - eg. E-mini S&P M0 1260C To be LONG in the butterfly (as above) is to buy the wings and sell the body, a SHORT Volaility strategy and receiving premium from writing the two ATM options. Best if the mkt stand still. The box is simply an arb. strategy, eg: The bull (call) spread half: +1 M0 1200C -1 M0 1300C AND the bear (put) spread half: +1 M0 1300P -1 M0 1200P Note the legs are NOT all calls or all puts, and that at expiry the paid out for the box spread will be 1000pts regardless where the underlying settles. So this is an arb. opportunity if you can buy the box spread below 1000/(1+i)^t then you have yourself a risk-free arb.

Sorry, I have some confusion. In the CFAI textbook, to create box spread they use Long a Call with X(L) Short a Call with X(H) Long a Put with X(H) Short a Put with X(L) So the initial outlay is CL - CH + PH - PL --> non zero (= (XH-XL)/(1-r)^t if correctly priced) But in level3aspirant’s case, to create box spread he uses LONG a call with X(L) SHORT a call with X(H) LONG a call with X(H) SHORT a call with X(L) Then the initial outlay will be CL - CH +CH - CL = 0 ?? Could someone explains?

Right I think I have it. Because the payoff on a box strategy is always x(h)-x(l), this must be equal to the premium otherwise there’s an arb. Do you discount x(h)-x(l) back to time zero to compare to the premium because the payoff is received at expiry but the premuim is paid up front?

yes u are right … the last 2 options in box spread should be puts. (sorry about typo error)

Chedges, Yes, we need to discount back to see if arbitrage opp exists. PV(XH-XL) = Initial outlay => box spread is correctly priced. PV(XH-XL) > Initial outlay => box spread is underpriced PV(XH-XL) < Initial outlay => box spread is overpriced PV(XH-XL) = (XH-XL)/(1+Risk free)^t

Just to understand box spread: Shall we calculate the profits both before and at expiration? How different are they? Are these options European or American ones?

How could any male on this thread not know what a box spread is? That’s the only term that stuck in my head from my first reading…

How does this relate to the risk free rate…if the return is less than the rf rate is it a buy and a sell if it is above. Or do you play it in terns of the PV of X-X vs the price? There is a Q on the Schweser Exam book 2 on this, didn’t quite get it.

skillionaire, pretty funny : ) I’m only going to remember that it’s going long a bull call and bear put spread, and they usually earn the Rf rate. They’re not going to ask for all this other s**t… we’re not taking an options exam.

I fully understand box spreads now. The payoff on a box spread will always always be Xh-Xl ( high strike price - low strike price). Have a go with some prices to see that this is always the case. Now if the payoff is certain no matter what, then surely the cost for the strategy should equal the payoff. otherwise there would be an arbitrage. Well thats what these questions are trying to determine. The cost of the strategy is the sum of the premiums on the four options. The payoff happens at expiry, but the premiums are paid up front so you need to compare the PV of the payoff to the premium. To calc the PV of the payoff you discount by the risk-free rate. If there’s a difference between the PV payoff and the net premiums, there’s an arb opportunity as the cost is different to the certain payoff value.

Are these options European or American?

African, but they’re non-migratory… I think the way a box spread works is, the “moneyness” of the bull call spread and the “moneyness” of the bear put spread always net to 0 plus the of the (1+RFR)^t * total paid premia - i.e., your return will always be (1+rfr)^t , regardless of the strikes. If the rate of return is NOT the RFR, you can earn an arb profit. Or, wine, roses, and soft music.