New Release 2016-FRR Financial Risk and Regulation Questions

The risk manager is analyzing a long position worth USD 10 million. To hedge this portfolio, the risk manager uses options that decrease in value by JPY 0.50 for every JPY 1 increase in the long position. This effectively means the options are shorting the currency. Therefore, if the long position is fully hedged by these options, the overall exposure of the portfolio will be equivalent to the full value of the long position but in the opposite direction. Thus, the portfolio has the same exposure to USD as a portfolio that is short USD 10 million.

The formula to estimate a partial change in an option's price based on the change in the underlying asset's price is primarily dependent on the option's Delta. Delta represents the sensitivity of the option's price to changes in the price of the underlying asset. Therefore, the most straightforward and widely used formula to estimate this partial change is:Partial change in option price=Δ×Change in underlying pricePartial change in option price=Δ×Change in underlying priceThis formula directly utilizes Delta to measure the immediate rate of change in the option's price relative to a small change in the underlying asset's price. The other options involving Gamma are more complex and not typically used for simple partial changes.

Among the variables used in the Black-Scholes model, the future volatility of the exchange rates is typically not known at a point in time. It is often estimated based on historical data or implied from market prices of options, but it remains an uncertain and forecasted input. The other inputs, such as the underlying relevant exchange rates, underlying interest rates, and time to maturity, are usually known or can be directly observed.

References:The inherent uncertainty in predicting future volatility is discussed in the context of option pricing in the "How Finance Works" document​​.

Model Definition: Credit scoring models are typically used to grade the creditworthiness of small- and medium-sized enterprises (SMEs).

Application: These models evaluate the credit risk of SMEs by considering various financial and non-financial parameters, providing a systematic and quantitative method to determine credit scores.​