How To Fix RY819 - Black-Scholes pricer: negative spot rate at opt. with & days to expiratn

SAP Error Message - Details

• Message type: E = Error

• Message class: RY - Messages for RM Basis

• Message number: 819

• Message text: Black-Scholes pricer: negative spot rate at opt. with & days to expiratn

What causes this issue?

Negative spot values might occur in a <ZH>regular</> way if some of the
following conditions are combined:
Options on interest rate instruments (such as caplets, floorlets,
swaptions or implicit options arising from bounded variable interests)
You have chosen the <LS>Swaption as Interest Rate Option (Black-Scholes
Model) </>valuation model (as opposed to the <LS>Standard</><ZK>
</>valuation model which values swaptions as bond options).
Yields are quoted less than zero
When an absolute but sufficiently large negative shift is applied,
either a market data shift or a shift from historical VaR simulation.
The following <ZH>irregular</> circumstance can also lead to negative
spots:
Forward calculation results in negative yields when the curve of
discount factors does not decrease monotonically.

System Response

The basic assumption of the Black-Scholes model that the spot price S(t)
is a positive number for which possible future values S(T) are
log-normally distributed is not applicable. An alternative assumption on
the distribution is not available.
The option price can still be calculated on the basis of the following
assumption:
Consider S(t)<0 as an extreme case with virtually zero probability that
S will increase beyond strike value K by expiration date T. In other
words: The probability of S(T)>K is so minute as to almost disappear.
The domain of the original Black-Scholes model can subsequently be
extended. In this way, the price function and its first derivatives
steadily continue beyond the original positive spot domain. Therefore,
sensitivity calculation, as well as delta and gamma calculation in VaR
runs will not suffer from indefinite numbers that would occur without
steady continuation.
Price formulas for the domain extension area S(t)<0:

The system issues an error message and will not allow you to continue with this transaction until the error is resolved.

Price value of a put:,,P = B(t,h,T) * [ K - S(t,T) ]
Price value of a call: ,,C = 0
where:
K: Strike price
S(t,T): expectation spot value on expiration date T
B(t,h,T): discount factor taking into account any horizon date h

How to fix this error?

Check yield curves and market data yields for inconsistencies.
If there are no irregular reasons for negative spots, you may consider
either keeping the Black-Scholes model and its domain extension or
changing the valuation model.
In the case of swaptions, for example, you can switch from the
<LS>Swaption as Interest Rate Option (Black-Scholes Model)</> to the
<LS>Standard</> valuation model. Or, for swaptions, caps, and floors,
you can use the <LS>Hull-White</> pricing method.

Error message extract from SAP system. Copyright SAP SE.

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• What is the cause and solution for SAP error message RY819 - Black-Scholes pricer: negative spot rate at opt. with & days to expiratn ?

  The SAP error message RY819, which refers to the Black-Scholes pricer indicating a negative spot rate at an option with a specified number of days to expiration, typically arises in the context of financial derivatives pricing. Here’s a breakdown of the cause, potential solutions, and related information:
  Cause:
  
  Negative Spot Rate: The error indicates that the model is encountering a negative spot rate for the underlying asset. This can happen due to market conditions where interest rates are negative, or if the input data for the pricing model is incorrect or inconsistent.
  Input Data Issues: Incorrect or outdated market data (like interest rates, volatility, or underlying asset prices) can lead to this error. If the data used for the Black-Scholes model is not aligned with current market conditions, it can produce unrealistic values.
  Model Limitations: The Black-Scholes model assumes certain conditions (like constant volatility and log-normal distribution of asset prices) that may not hold in all market scenarios, especially in volatile or unusual market conditions.
  
  Solution:
  
  Check Input Data: Verify the input parameters for the Black-Scholes model, including the spot price, strike price, time to expiration, risk-free interest rate, and volatility. Ensure that these values are accurate and reflect current market conditions.
  Update Market Data: If the spot rate is negative due to outdated or incorrect market data, update the relevant market data in your SAP system. This includes interest rates and any other financial indicators that may affect the pricing model.
  Review Configuration: Check the configuration settings in your SAP system related to financial instruments and derivatives. Ensure that the settings are appropriate for the current market environment.
  Use Alternative Models: If negative interest rates are a common occurrence in your market, consider using alternative pricing models that can accommodate such conditions, such as the Black-Scholes model with adjustments for negative rates or other models like the Heston model.
  
  Related Information:
  
  Black-Scholes Model: Understand the assumptions and limitations of the Black-Scholes model. It is primarily used for European options and may not be suitable for all types of derivatives.
  Market Conditions: Stay informed about current market conditions, especially regarding interest rates and volatility, as these can significantly impact option pricing.
  SAP Documentation: Refer to SAP’s official documentation or support resources for specific guidance on handling financial errors and configuring the pricing models correctly.
  Consult with Experts: If the issue persists, consider consulting with financial analysts or SAP experts who specialize in derivatives pricing and financial modeling.
  
  By addressing the underlying causes and ensuring that the input data is accurate and relevant, you can resolve the RY819 error and successfully price options using the Black-Scholes model.