Doubts- FRM P2

[saurav_m_cse]

Hi David,
Hope you are doing good.
Below are few questions which I want to clarify.

1. Based on the Implied Volatility, the OTM Put or ITM Call is undervalued. ( I am assuming the regular left skewed Volatility Smile in this regards). Please correct if I am wrong.

2. Which Option has the Largest Negative Vega?
My understanding is , if nothing else is given the answer would be barrier options.

3. How can we represent , Chooser option as a function of Plain Vanilla option ? Given Strike Price, Risk Free Rate and Time to Maturity

4. We know some of the weakness of VAR (like it does not follow Sub Additive and hence not coherent) but what are the weakness of Expected Shortfall ?

 

[ShaktiRathore]

Before David clarify in detail, I may like to answer:
1. This is different for different like currency option has volatility smile which implies that the both otm/itm options are overvalued,on the other hand for equity option with volatility smirk implies itm call and otm put are over valued http://forum.bionicturtle.com/threads/hull-19-02.6390/#post-26816
2. I too think so the down/up and out barrier option have high negative vega but look out for other options too.
3. It's call and put combination I think
4. ES has difficulty in backtesting due to lack of data points as compared to var,Es is difficult to compute while var is a simple measure
Thanks

 

[saurav_m_cse]

Thanks Shakti.
I have a doubt with regards to # 1. My understanding is that, because of the implied volatility, the OTM/ITM currency options are actually undervalued. The BSM predicts a Implied Vol of Straight line where as in the reality we have the smile or smirk. So does not that mean that the theoretical price of those options are less than the market price. That means they are undervalued ?

 

[djh2121]

Saurav you're almost right. The vol smirk or smile means that the theoretical price of the OTM/ITM options would be less than the market price if we used the ATM implied volatility (i.e. a flat vol curve). This is because traders believe there is a greater probability of large moves in the underlying than implied by the lognormal distribution. This manifests in the market as high option premiums.

Now, here's the trick, in order to make the BSM consistent with market prices traders will back out an implied volatility for each individual strike that makes the model price consistent with the market price. (Remember since the volatility parameter is unobservable it is essentially a free parameter that can be varied.) This process of backing out an implied vol for each strike is what creates a vol curve that is consistent with market prices for every traded strike. Depending on which strikes have high premium (relative to a flat vol curve BSM world) this could create a vol smile, smirk, or even a frown.

The basic intuition is that option premium and implied volatility are analogous. If an option has a premium that is greater than what would be predicted by a flat curve then its implied volatility must be higher as well. Conversely if the premium is lower than what would be predicted by a flat curve model, then its implied volatility must be lower.

 

[David Harper CFA FRM]

djh2121 I read your post twice already, I've tagged it for future reference and sharing: I think its one of the clearer (elegant) explanations I've read, thank you!

 

[saurav_m_cse]

@djh2121: I guess your explanation went beyond the theoretical concepts covered in FRM. Great ! .

Well , for exam purpose , I think that given a choice which option is undervalued, I could choose the deep OTM Put or deep ITM Call (in case of equity option) and ITM/OTM Call / Put for currency option.

 

[djh2121]

David, thank you for the compliment.

saurav, your statement is correct if you are given that the volatility used to value the ITM/OTM option is the ATM implied volatility. Without knowing what volatility is being used, any option on the chain (ITM/OTM/ATM) could be under/over/correctly valued relative to its market price. Therefore asking which option does BSM undervalue without first specifying a volatility assumption isn't a well formed question.

Try the following question to see my point: Assume that a risk manager values all of the Jan-14 AAPL options using the BSM model and the implied vol of the put with the lowest traded strike price (i.e. the most deeply out of the money traded put). Which of the following JAN-14 AAPL options will be overvalued relative to its traded market price: (a) ITM put (b) ATM call (c) Both (d) Neither

I think this would be the kind of question that GARP could ask to query this topic and put test-takers who have simply memorized ITM/OTM under/overvalued off-balance. Hope you find this helpful.