Upper Limit on Range Forward

case1.md

4. Upper Limit on Range Forward

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(20%) Employing the spot rate version of the Black-Scholes foreign exchange valuation model, determine the appropriate value of the upper limit of the range forward on the NZD recommended by Banco Manquehue. This requires a trial and error procedure. Confine your answer to three significant digits.

Recall that to apply the Black-Scholes model in a situation where bid-ask and deposit/borrowing rate spreads exist, the midpoints of said spreads must be used. As well, note that a range forward has a value of zero at inception and that a range forward may be viewed as an option collar.

Value for buy forward range

When $ P(X = L) = C(X = U) $

where $ P(X=L) $ is the put premium when the strike price equals the lower limit and $ C(X = U) $ is the call premium when the strike price is at the upper limit.

Input for Black-Scholes calculation

'strike price':     CHP 80/NZD
'spot rate':        CHP 95/NZD
'volality':         20%
'risk free yeild':  3%
'dividen yeild':    6%
'expiry':           1.5 (years)

Results from deltaquants.com Black-Scholes calculator

'put premium': 3.824CHP

using trial error process, equivilant Call Strike Price for a premium of 3.824CHP is about

'strike price': CHP 105.29/NZD