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Choosing Strikes for a Costless Gold Collar

Article Quant Q&A · Author: Ian Calvert
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Summary

The note explains how to select strikes for a costless collar using gold options. A collar pairs a long put with a short call whose premium offsets the put’s cost. There is an unlimited set of such strike pairs: for each positive put strike, a call strike can be chosen so the two option prices match. The put strike lies below the forward price, while the call strike lies above it.

The forward can be observed in over-the-counter forward or futures markets, or estimated from spot, interest rates, and gold storage costs. Once the put strike and forward are known, the matching call strike depends on the relative implied volatility of out-of-the-money puts and calls. For example, higher implied volatility on calls can require a call strike farther above the forward than the put strike is below it. The note gives no specific volatility surface, strikes, prices, or valuation model. It also cautions that gold-market skew can shift substantially with market conditions, so a strike relationship inferred at one time may not persist.

Key ideas

  • A costless collar matches the premium of a long put with the premium of a short call.
  • The put strike is below the forward price and the call strike is above it.
  • Gold forwards can be observed in forward or futures markets or estimated from spot and carrying costs.
  • The call strike needed to offset the put premium depends on implied volatility skew.
  • Gold option skew can change significantly as market conditions change.

Tags

OptionsCommoditiesVolatilityDerivatives pricing
Full text
# Estimate The Interval For European, Say 6 month, At-the-Money, Gold Price Collars


# Estimate The Interval For European, Say 6 month, At-the-Money, Gold Price Collars












Hopefully these are acceptable questions in this forum.

I assume such options are today OTC instruments only with significant corporate risk on the miner. I have a little knowledge of interest rate modelling and derivatives et al. but none of gold or other metals.

For (gold) miners, with significant debt, there are underlying practical risk management questions . References to simple models including any related tradeable instruments would be of interest

## Answer by dm63 (score 0, accepted)

https://quant.stackexchange.com/a/30999

There is an infinite set of pairs of strikes that form a costless collar, since for each (positive) put strike there is a call strike that makes the put price equal the call price. Within each pair, the put strike is less than the forward price and the call strike is greater than the forward price. The forward price of gold can be observed from otc forward markets or futures markets, and it can be calculated from spot price, interest rates and gold storage costs. Given a put strike and a forward, the call strike for a costless collar depends on the skew for out of the money puts versus out of the money calls. For example, if the out of the money calls on gold are at a much higher implied volatility than out of the money puts, then the call strike will be further from the forward than the put strike. Skew in the gold market (like other otc markets) can move significantly depending on market conditions at any given time.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.