In this workout, we need to use the Black-Scholes calculator provided to answer the questions. The Black-Scholes calculator has the various inputs into the Black-Scholes formula and then the output is the raw price. And you can see in cell J8 there's a very long formula there, which is calculating that raw price. And then in column K, we also have the percentage of base price. The first thing we need to do is price the following risk reversal using the vol price quotes given we have two different options here. One is a put option and the other is a call option. Now if you take a look, all of the other inputs into the Black-Scholes calculator are the same as what's already there except for the strikes, the put versus call and the vols. So in order to price these two options, all we need to do is copy in the relevant information up into the calculator and then pick up the percentage base price. Let's do the put first. We'll copy up the strike.

We then need to change the type from C for call to P for put.

And the vol is not 7.8% for this put it is 8.2%. So let's copy that up and we can see that we have a raw price of 0.0085, but percentage base is 0.782% and that's what we want. So all we need to do is copy this and then we need to paste special as values because we don't wanna copy that formula across. So I'm just gonna paste special values to get that 0.782% price.

And we need to do exactly the same thing for the call. So the call has a strike of 1.13, copy that up.

We then need to change from a put to a call, so changing P to C and the vol is 7.8%, so I'm just gonna copy that up and we get our percentage base price of 0.95%. We're gonna copy that down and again, paste as values.

So that's the first part of this workout done. What we need to do next is quote the net premium in euro to our client and we're told that in this risk reversal, the client is buying the call and the notional is 10 million euro.

We've got the two options, the 1.05 put and the 1.13 call, we can now link to the prices that we've just calculated. So if we pick up the put first, it's the 0.782% and I can just copy that down to pick up the price of the call.

Notional, we can just hard code in here, 10 million euro and copy that down.

And then to work out the price in euro, it's as simple as multiplying the percentage base price with the notional because remember the whole purpose of that percentage base is that the price is already in terms of the base currency, which in this case is euro. And so there's no conversion necessary. So we get 78,000 as the price of the put. And if we copy that down exactly the same calculation, we get about 95,000 as the price of the call to work out the net cost to the client. We have to look at which of these two options they are buying in this risk reversal and which they are selling. In this case, we are told that the client is buying the call, in which case they will have to pay the call premium and they are therefore selling the put, which means that they would receive the put premium. And so the net cost to the client is what they would pay minus what they receive. And that gives us a cost of around about 17,000 euro.

The last part of this workout asks if the client wants a 0 net premium, what is the call strike for zero cost, assuming the same vol works So we are not changing the strike on the put and therefore the price of the put will remain at 0.782%.

If the client wants a 0 cost position, then I need to make the strike on the call such that the price of the call is 0.782%.

Now we could do this by trial and error by going into the Black-Scholes calculator and changing the strike on the call until we get a price of 0.782% at the moment at at a 1.13 strike, the price is 0.95% and we need to lower that price in order to lower the price on a call, you increase the strike so we could go increase the strike and see what it would need to be to get 0.782% price. But a more efficient way of doing it would be to use goal seek. I'm just going to move up so we can see the calculator then to access goal seek, it's under data what if analysis. And there we see G for goal seek.

We already have the relevant details for the call in the pricer, but now we need to tell Excel, okay, what do we want the outcome to be and what do we need to change in order to achieve that outcome? We want to set the percentage of base to be 0.782%. So we are gonna set cell K8 and the value we wanna set that to is 0.782%. And then which cell do we want to change in order to achieve that 0.782%. We want to change the strike on the call, so that's going to be G8. And if we press, okay, we'll see that the strike has changed to 1.1413, but the percentage base price is 0.705% and that's not accurate enough. We wanted it to be 0.782% or as close to that as possible. Now this can be rectified by changing the level of accuracy in our formula settings. So let's get rid of the goal seek for now.

I'm going to go into my settings. So file options or you could use your accelerator keys alt ft.

And we are gonna go into formulas. And you can see here under maximum change it's 0.001. I'm going to change that to zero point. Just add in, say three or four zeros. Let's click okay and run the goal. Seek again and see what it does this time. Okay, so I'll use my mouse this time instead of the accelerator keys, it's data what if analysis and then goal seek.

And we're going to repeat that calculation. We want to set cell K8, which is percentage base. We want to set that to 0.782% and we want to do that by changing the strike, which is G8. If we now hit okay, we are much happier because we can see that we now have that 0.782 percentage base and a strike of 1.1375. The last thing I'm just going to do here, I think it's unrealistic to have a strike with all those decimals. If you look up at the top in our formula bar, that isn't 1.1375, it's got loads of decimals on the back of that.

So what I'm going to do is just type over that 1.1375 to get rid of all of those decimals.

And when I hit enter, you're going to see that percentage base price over here changes slightly because we are getting rid of all of those decimals. So it's not gonna be 100% accurate to give us 0.782%. We're going to get 0.781%, but that is good enough. I mean it's as close to 0 cost as anything. So if here we just finish up in row 27 by saying we need that 1.1375 as the strike on the call.

And so our price, if we just go pick that up from the calculator 0.781% and paste values. And so there we have a net zero cost or slightly actually positive for the client because the premium on the put they'll be receiving is slightly more than the premium on the call.