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# OPTION PRICING

# What is Kooltra Option Pricing?

Kooltra option pricing allows users to calculate the current value and risk metrics for Foreign Exchange (FX) Options on the Kooltra platform. Currently, there are two apps that support Option Pricing:

- Kooltra Pre-Trade Option Pricing
- Kooltra Post-Trade Option Pricing App

The differences between these two apps as well as their intended uses are highlighted below.

## Kooltra Pre-Trade Option Pricing

What is Pre-Trade Option Pricing?

Pre-trade option pricing is intended for users who want to value or calculate risk metrics of an option without creating the option in Kooltra. Some simple examples of how this service can be used include:

- Validating the price of an option quoted by a counterparty
- Determining the spread to apply on an option before providing a quote
- Identifying the delta-adjusted market exposure of an option before trading. This will help ensure compliance risk limits are not violated
- Validating against internal option pricing models

How do I use Pre-Trade Option Pricing?

After your administrator has enabled the pre-trade option pricing app, you can access the pre-trade option pricing page by selecting the FX Option Pre-Trade under the FX Options category. This should take you to a page that looks similar to the following:

To use the service, simply enter the details about the option that you would like priced and click Calculate:

You are also able to deal an option directly on this page. For example, if you enter the details of the option and are content with the valuation returned, you can click Deal, specify the additional information about the option, and then it will be added to Kooltra:

## Kooltra Post-Trade Option Pricing

What is Post-Trade Option Pricing?

Post-trade option pricing is intended for users who want to value or calculate risk metrics of an option after it has been inserted in Kooltra. Some simple examples of how this service can be used include:

- Calculating the current value and mark-to-market of each option in your portfolio in real time
- Viewing aggregated delta-adjusted positions of each currency pair for your options in real time

How do I use Post-Trade Option Pricing

In order to use post-trade option pricing, your Administrator must configure the Post-trade option pricing app and enable Kooltra Post-Trade Option Pricing. Once enabled, you can enter your options into the system as usual and the Post-Trade app will continue to update the price of all options in the selected entity's portfolio.

After the options have been priced, you can navigate to FX Options under the FX Options category and the last two columns should display the current valuation and mark-to-market of the options:

For more details on a particular option, open the option details by clicking on the ID in the Trade Name column, and navigate to the Risk tab. This tab should display the current valuation, any risk metrics that are available on the option, and the last time that the option has been valued. In addition, you can recalculate the option valuation and metrics on this page by clicking recalculate:

How does Post-Trade Option Pricing work?

When an option is submitted, the Post-Trade Option pricing app will schedule a job in the future to price all of the options under the entity. As a default, the job will be scheduled for fifteen minutes in the future but this value can be configured by speaking with your administrator. Provided there are open options in the entity's portfolio, these options will be revalued every fifteen minutes from Sunday at 5:00pm EST to Friday at 5:00pm EST.

# What Options are Supported?

Currently, the pricing service will support any of the following options for expiration dates up to one year and for the supported standard currency pairs (See Appendix 1) and their inverses:

- European Vanilla FX Options
- European Single Barrier FX Options
- Currently barrier end date must be the same as the expiration date but the barrier start date can be any time during the life of the option

- European Double Knock-In/Knock-Out FX Options (i.e. we do not currently support Knock-In-Knock-Out (KIKO) Double Barrier Options)
- Currently barrier end date must be the same as the expiration date but the barrier start date can be any time during the life of the option

# What Valuation Models are Supported?

For now, valuation models are limited but these will be expanded in the future. Currently, the available models, as well as the types of options that they support on Kooltra, include:

Black-Scholes (Garman-Kohlhagen):

See the high-level overview of the Black-Scholes model for a detailed explanation of the model, the assumptions, and the limitations.

Resources:

- A high level overview of the model: Options Pricing: Black-Scholes Model
- Derived greek formulas under the Black-Scholes framework: Black-Scholes Formula Parameters
- Formulation of the Black-Scholes model: The Black-Scholes-Merton Approach to Pricing Options

Supported Option Types:

- European Vanilla Options

Vanna-Volga:

The Vanna-Volga model improves upon the Black-Scholes model by attempting to alleviate the unrealistic assumption of constant volatility. It prices FX Options by creating a replicating portfolio similar to the Black-Scholes replication portfolio (See Formulation of the Black-Scholes model under Black-Scholes) but it dynamically hedges the risk associated with the option's vega, vanna, and volga. The three option greeks are described below:

- Vega: The sensitivity (partial derivative) of the option price with respect to the volatility parameter or implied volatility (See "What is implied volatility" in Resources)
- Vanna: The sensitivity of vega with respect to the current market rate
- Volga: The sensitivity of vega with respect to the volatility parameter or implied volatility (the second derivative)

Resources:

- What is implied volatility: Implied Volatility
- Technical Overview of the Vanna-Volga Model: Vanna-Volga methods applied to FX derivatives: from theory to market practice (See section 4 on Vanna Volga. Prior sections provide supplementary knowledge on market conventions)

Supported Option Types:

- European Single Barrier FX Options (Barrier end date equal to expiration date)
- European Double Knock-In/Knock-Out FX Options (Barrier end date equal to expiration date)

### Appendix 1: Supported Standard Currency Pairs

- AUDUSD
- EURCAD
- EURGBP
- EURUSD
- GBPCAD
- GBPUSD
- USDCAD
- USDJPY
- USDCHF

Option Pricing, pre-trade pricing, post-trade pricing, risk, delta