Risk-neutral density from spot prices?

Question

I am currently working on a university project and I hope someone can help me out with a rather silly question :-) I want to analyse the change in the shape of risk-neutral density functions of spot GBPEUR before Brexit. I've chosen as potential dates May 1, 2015 and May 1, 2016. What data should I gather from Bloomberg? As aware as I am, Bloomberg would give me the volatility skews but not the risk-neutral densities of course. So, by using MATLAB, how can I get the risk-neutral density? What data should I get?

I was thinking of using this MATLAB app: https://uk.mathworks.com/company/newsletters/articles/estimating-risk-neutral-density-from-option-prices-with-a-matlab-app.html , but I would like to receive some advice about the data that I need to use.

Many thanks!

Answer 1

Retrieving the Risk Neutral Density from option prices is nicely developped by Figlewski and Birru here . Very basically what you will need is the spot price of options, their respective strike/type/IV (for the cubic splines), and the risk free rate

Answer 2

Do a quick search on this site to see how the risk neutral cumulative distribution function is related to the derivative of vanilla option prices with respect to strike.

In your case you would have for the EURGBP risk neutral CDF $$ P(\text{EURGBP}_T \leq K) = 1 - \frac{d}{dK}\text{Call}_{\text{EURGBP}}(T, K) / \text{discount}_{\text{GBP}}(T) $$

Answer 3

As mentioned in the two answers you can use option prices to do so.

What data should I gather from Bloomberg?

• In the search function you can type GBPEUR Crncy.
• Type OVDV and type enter which takes you to the Option volatility surface. Read about it here http://www.fintute.com/2013/06/15/option-volatility-surface-bloomberg-training/#.XI_vfa0kqEI
• Adjust the date and then you have different Implied Volatilities given for different Time to maturity and strike. The strikes are given by Delta which you can compute to Moneyness. See my old question: Calculate strike from Black Scholes delta
• You can compute the option prices by the Black Scholes formula where the volatilities are the implied volatiles in your data.

When computing the options prices then be aware to use the correct interest rate. See: https://www.researchgate.net/publication/275905055_A_Guide_to_FX_Options_Quoting_Conventions

This one way to get option prices from Bloomberg. This is possibly not the only nor best way. That I don't know.