Trial and error and interpolations

Hi all,

For the options questions, a usual type of question would be to derive the value of a particular parameter given some "target value".

e.g. we are given the price of a European call option and were asked to find the implied volatility.

Apart from the trial and error approach, are there any other ways to avoid the heavy use of calculator? (with the BA calculators, I often press the wrong buttons!)

With the above example, the calculations are:
1) specify sigma, calculate d1,d2
2) interpolations on phi(d1) and phi(d2)
3) find first call price
4) specify another value of sigma and calculate d1,d2
5) interpolations on phi(d1) and phi(d2)
6) find second call price
7) interpolate the call prices against the true price to find correct value of sigma

(That's 4 times of looking up values in the stats table and 5 interpolations.....I'm spending 10 mins in practice just to do the above cals for 3 marks, given no handling error!! )

And for the trial and error approach, what's a smart choice of the first trial value? And after specifying the first value, how much apart should we select the second value from the first one (in units of 0.1)?

0.5 may seem a good starting point for sigma. What about r? K (relative to S0)? and q?

Thanks!!

 

Trial & error it is - and lots of practice.

In theory you could program B-S on an HP12c and find the implied volatility much more quickly; on the other hand, you'd have to learn to program the HP12c.

The other thing that is worth learning to do if you have the fx-85 model is using the linear regression mode to interpolate. Once you get the hang of it it's much less error prone.

 

Thanks guys for the reply!

How would you go about choosing the first value to test?

i.e. if they ask for implied volatility, what value will you try at first?

Or would you just blind guess the first one then choose the second one according to the relationship between the parameter and the option value? (e.g. volatility is proportional to call/ put value; K is proportional to the inverse of the call value.)


Thanks!!

 

For an implied volatility, I'd suggest always starting with 20%, ie 0.2, unless there is some suggestion in the question (explicit or otherwise) to use a different value. This is because:

(a) 20% is a fairly realistic value

(b) the answer in exam questions is often close to 20% and occasionally exactly equal to 20%!