Currency options Hedging against money received in the future

[sultan90]

Hi first question here so i apologize if it is in the wrong section.
I had a question about money received in the future in pounds , but need to be in USD. assuming USD is weakening against the pound My assumption would be to either buy a put option or sell a call option to hedge against any fluctuations.

assuming the amount to be received is $1,057,500 and the strike we chose is $1.45/pound current exchange rate is $1.488/pound with a premium of 0.044 (each contract is in 12500 pounds increments)

How do i calculate the cost and the potential profit of this put option contract?

my answer would be to calculate the cost of the contract as well as the premium to find the number of contract i take 1,057,500/12500= 85 contracts roughly
premium cost = 85*12500*0.044=46,750
contract cost = 85*12500*1.45 = 1,540,625
money received if put is excersized at 1.45 rate = 1,057,500 * 1.45 = 1,533,375
Then i take the cost from money received to find the profit margin. I am i on the right track here?
Appreciate any help.

 

[David Harper CFA FRM]

Hi @sultan90 Welcome!

Do you have the full question, can you share it? In any case, I assume you mean that the underyling exposure is the expectation to receive £1,057,500 (not dollars). I agree with much of what you wrote. Specifically:

• If we expect to receive £1,057,500, then one hedge is the buy the put option to sell £1,057,500; and if each contract is to sell £12,500, then we can buy £1,057,500/£12,500 = 84.60 puts ~= 85 contracts (this is not a delta neutral hedge, btw. There are other hedge ratios ....)
• The option premium (initial) cost = 0.044 * 85 contracts * 12,500 per contract = $46,750; i.e., agree with you
  
• At future FX spot of $1.45, there is no intrinsic value, so I will use a lower future spot rate. Say the future FX rate is $1.40.
  • Payoff from option exercise = max[0,(1.45 - 1.40)] * 85 * 12,500 = $53,125
  • Loss on underlying = ($1.40 - 1.4880) * £1,057,500 = -$93,060.
    
  • So we'd typically say the option payoff is 53,125 but option profit is $6,375 = 53,125-46,750, and the net hedged position loss is -93,060 + 6,375 = -86,685.
    
  • But that's pretty much our maximum downside. In fact, the max net hedged downside is at future $1.45 where underlying loss is ($1.45 - 1.4880) * £1,057,500 = -46,750 such that loss plus option premium equals -86,935 (slightly worse than above). That's the bottom, any lower on the future FX spot and it only gets a little better (as they are almost 1:1). I hope that helps. Please feel free to share the full specific question and we can verify assumptions etc? Thanks!

 

[sultan90]

Thank you so much David for the replay as It makes things a lot clearer. One of the assumptions is that they included 6% profit margin in the account receivable. The question asks about the best potential profit for a receivable in the future , assuming the currency is depreciating. We are asked to find the the profit margin if we stay unhedged , using forward and using options. I calculated unhedged and forward hedge.

My question now is how do i compare this to the money received in the future. They used 1.482 initial spot rate to calculate the amount of
pounds 1,057,500*$1.482= $1,567,215(they included a profit margin of 6% and want to keep it)
Should i just assume the worst case and multiply 1.45 * 85 * 12500= 1,540625 (The worst they can get) - the premium cost(46,750) then take the difference between 1,567,215-1,540,625?

Lastly, If I choose the other alternative option which is selling a call. Should i be going with a strike price lower than 1.482 like 1.45 or go up and choose 1.5; i am bit confused on someone buying a call on the other side when i choose selling a call.

 

[sultan90]

I meant .45 * 85 * 12500= 1,540625 (The worst they can get) - the premium net(86,685)*

 

[David Harper CFA FRM]

Hi @sultan90 I'm happy to help but you are dribbling out the assumptions. For example, I don't know how the 6% figures in, exactly. It's not +6% of the previous assumption, that i can see. On the other hand, i notice that 1.4880 - 0.0060 = 1.4820. We're happy to help: I can quickly imput my scenario in an XLS sheet (I think you should input this into a simple spreadsheet), but I'd want to see the whole, complete question. Also, it's just transparent. Good form is to share the complete question and the source. Another motive, I will tell you, is that many questions contains mistakes, and such questions can have people wasting time looking for a solution that does not exist. For example, you mention forwards. Maybe the solution should include writing a put (as we are doing) and forward, rather than writing a put and a call (it's not clear to me how writing a call will be a hedge, unless you write a call with a higher strike price; then the premium collected reduces net loss on the down side. That's not really a hedge, it's income enhancement). Let me know, thanks!