Are you pricing FX Basket Options correctly?

Back in January 1994, Bruno Dupire presented his paper 'Pricing with a smile' (click here) later recognize as the Local Volatility model, widely implemented in the banking industry.

Since then there has been an increased complexity of the Financial Derivatives instruments, bringing new challenges to Quants, including to both Bruno Dupire and Fabio Mercurio groups at Bloomberg.

Examples are the pricing and hedging of FX Dual Digitals, FX Basket Options and FX Spread Options, with the need to capture the terminal smile distribution of all triangular crosses.

Why?

The arbitrage-free triangular rule in FX applies when decomposing the ATM volatility of a cross via a third currency, with the correlation represented by the angle of two sides of the triangle.

However such rule stops working for OTM volatility in the presence of a market skew and therefore conventional models cannot fit the smiles of all crosses.

'Local Vol Local Correlation' model calibrates to both ATM and OTM triangular FX volatility smiles.

The 'Local Vol Local Correlation (LVLC)' model is available to all Bloomberg Anywhere desktop users.

Step-by-step guide.

Type DLIB <GO> in your Bloomberg terminal.

Launch the ‘Dual Digitals’ FX Template

At the bottom of the screen, select the model ‘LVLC – Local Vol Local Correlation’

Click on ‘Calculate’.

The valuation is done through a Monte Carlo simulation, in this case using 20,000 paths.

To check the calibration errors against all 3 cross-currency volatility smiles, go to the ‘Calibration’ tab.

Under the ‘Asset’ drop menu, select the currency pair to report the calibration errors. Change the 'View' to 'Table' in order to export the results to Excel.

Try the same exercise for your FX Basket options and compare the results against other conventional models, available in DLIB as well.

For more information, don't hesitate to contact our Analytics desk by typing <HELP> twice on your Bloomberg keyboard.

Bonus feature!

As a bonus, you can create your own DLIB template and share with other users.

Type DLIB <GO> and go to the 'BLAN Scripts' section.

Select a payoff and launch the example script, in this case ‘Dual Digitals’.

You can do alterations to the payoff.

Click on ‘Create Deal Template’.

Confirm one of the two choices in the notification page.

You now have the deal parameters on the left side, where you can do any fine tuning.

Click on ‘Validate Template’.

Congratulations! You have created your first new DLIB Template.

To know more about our 'Local Vol Local Correlation' Model, please type 'DRVP <GO>' at your Bloomberg Terminal and check the 'White Papers' at the 'Derivatives Library (DLIB)' section.