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### Negative Strike Price

Posted: **August 21st, 2019, 9:27 pm**

by **SWilson**

Using a plain vanilla black scholes option model how would one handle a negative strike price as it relates to, a basis of, underlying. So the basis differential can float from negative to positive but the strike is always negative. I was thinking of converting the prices to the outright amounts but was wondering if anyone else has ran into this. Thanks.

### Re: Negative Strike Price

Posted: **September 4th, 2019, 3:15 am**

by **doublebarrier2000**

if the underlying is a basis, I would suggest a spread option model of some nature.

; but you add a displacement (assuming S + d is log normally distributed) and re-calibrate your smile parameters. This is how negative rates & strikes are dealt with

### Re: Negative Strike Price

Posted: **September 5th, 2019, 9:59 am**

by **Collector**

"Using a plain vanilla black scholes option model how would one handle a negative strike price"

\begin{equation}

p(-S,-X,T,r,-\sigma)=c(S,X,T,r,\sigma)

\end{equation}

not exactly what you asked for, but interesting enough! But will not let the basis differential float from negative to positive. Numerical method...

### Re: Negative Strike Price

Posted: **September 5th, 2019, 3:25 pm**

by **Paul**

You can use any model or formula you like. The question is whether there is any rigorous (ish) justification. There’s usually a stage in the modeling involving hedging. If you can’t use that then your foundations are weak.

### Re: Negative Strike Price

Posted: **September 5th, 2019, 8:53 pm**

by **Collector**

You can use any model or formula you like. The question is whether there is any rigorous (ish) justification. There’s usually a stage in the modeling involving hedging. If you can’t use that then your foundations are weak.

Hedging at the university campus under ideal conditions, or in practice?

- Screen Shot 2019-09-05 at 6.37.16 PM.png (200.68 KiB) Viewed 4661 times

### Re: Negative Strike Price

Posted: **September 5th, 2019, 9:02 pm**

by **Paul**

If you can’t even do it on campus...!

### Re: Negative Strike Price

Posted: **September 5th, 2019, 9:12 pm**

by **katastrofa**

add a displacement (assuming S + d is log normally distributed) and re-calibrate your smile parameters

What d(isplacement)? Any number? Taken out of your or your colleague's arse?

I'm not sure which language in Google Translate I'm supposed to use to understand what "a negative strike price as it relates to, a basis of, underlying" means. If the negative values are rubbish, why not skip them? If not rubbish, e.g. a difference of two prices, k1-k2? - why not model k1/k2?

Wow, someone's talking about finance on Wilmott Forum...

### Re: Negative Strike Price

Posted: **September 5th, 2019, 9:19 pm**

by **SWilson**

I will speak for myself, this is in practice and just working on pure mechanics right now. Philosophical rigorous (ish) justification is next. In the past 6 months I've seen more exotic deals than ever, feels like out of nowhere.

Anyways, Espen, I've used your works to create and code models that have helped me tremendously. So thank you.

Paul, your work has guided me over my career as well and currently reading your Machine Learning book. Thank you as well. Did you ever think Larry ("what asset class looks cheap") Kudlow would be the US Director of the National Economic Council after your epic interview on CNBC?

### Re: Negative Strike Price

Posted: **September 5th, 2019, 9:39 pm**

by **SWilson**

add a displacement (assuming S + d is log normally distributed) and re-calibrate your smile parameters

What d(isplacement)? Any number? Taken out of your or your colleague's arse?

I'm not sure which language in Google Translate I'm supposed to use to understand what "a negative strike price as it relates to, a basis of, underlying" means. If the negative values are rubbish, why not skip them? If not rubbish, e.g. a difference of two prices, k1-k2? - why not model k1/k2?

Wow, someone's talking about finance on Wilmott Forum...

So they way it works is say you have 2 different oil market locations. Spot1 is $55 and Spot2 is $50. Right now we have a -$5 basis differential and I bought a put or call option with a (negative)$5 strike on the basis diff. As long as both prices stay negative the model is fine but if your basis flips to positive, Spot 1 is less than Spot2 now, it doesn't. UPDATE: I can work around this, but it's tedious, I was wondering if there is already a unified model for this scenario.

### Re: Negative Strike Price

Posted: **September 5th, 2019, 10:06 pm**

by **Paul**

Larry Kudlow!! I had a long chat with the production team before that. They laid out exactly what they wanted to discuss. And then I got some unrelated question! You can see the panic on my face as I was thinking how can I get from this topic to what they said they wanted to talk about!

### Re: Negative Strike Price

Posted: **September 5th, 2019, 10:23 pm**

by **Alan**

So they way it works is say you have 2 different oil market locations. Spot1 is $55 and Spot2 is $50. Right now we have a -$5 basis differential and I bought a put or call option with a (negative)$5 strike on the basis diff. As long as both prices stay negative the model is fine but if your basis flips to positive, Spot 1 is less than Spot2 now, it doesn't. UPDATE: I can work around this, but it's tedious, I was wondering if there is already a unified model for this scenario.

If the spreads are more-or-less normally distributed, maybe the Bachelier model makes more sense here. In that, the underlying lives on the real line and the model doesn't care about the signs of strikes. With [$]r \ge 0[$], formulas can be found, for example,

here. IMO, a better model to start with for this problem than using kludgy "displacements" and Black-Scholes.

### Re: Negative Strike Price

Posted: **September 6th, 2019, 2:27 pm**

by **SWilson**

Thanks Alan. I'm looking through this now.