**Limits on Value-at-Risk (VaR)**

- Any appropriate VaR methodology
- VaR methodology adopted should account for equity price risk, interest rate risk, credit (spread) risk, (foreign) currency risk, etc.
- Modelling should account for non-linear movements in securities, e.g. options and also volatility effects.

- VaR metric:
- With 99% confidence,
- Over 20 business days, and with
- 3 years of data

- Relative VaR (against reference portfolio/benchmark ~ if appropriate)
- VaR limit at 200% the reference portfolio)

- Absolute VaR
- VaR limit at 20% the portfolio value

If the above limits are breached for 5 business days, this must be reported to portfolio management with corrective steps proposed/implemented.

**Require a risk management ****program**** as well ****appointing**** a derivatives risk ****manager**

**Various reporting is required (to SEC & others)**

**Exceptions are available**

- If an exception is gained, the derivative exposure must remain below 10% the portfolio value

**Additional requirements**

- Identify derivative securities & their risks
- Guidelines must be available for the derivative(s) risk
- Stress testing must be performed on the portfolio
- Backtesting must be performed on the portfolio

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**Three types of models:**

-local volatility models,

-stochastic volatility models and

-deterministic volatility models

**Local volatility models** assume the volatility is constant (standard deviation) and hence a function of price and time. The local volatility model is therefore considered a generalisation of the Black-Scholes model.

**Two factor stochastic volatility model** (Stochastic Alpha Beta Rho – Sabr):

− Assumes volatility is stochastic, Sabr (ρ, υ).

Beta fixes the underlying volatility process and is fixed at 80% for equities, 0 for IR (volatilities are Gaussian) and 1 for currencies (volatilities are lognormal)

**Three factor deterministic volatility model** (Quadratic – Quad):

− Quad(ρ, υ, γ) – no assumption on the dynamics of the volatility process.

**Four factor deterministic volatility model** (Stochastic Volatility Inspired – SVI):

− SVI(ρ, υ, γ, ξ) – no assumption on the dynamics of the volatility process

Most South African banks seem to use **deterministic models** with up to 6 factors.

**References: **

A lot of research has been published by Dr Antonie Kotzé…

http://www.quantonline.co.za/publications_and_research.html http://www.quantonline.co.za/documents/Volatility%20Surface%2025%20Feb%202011.pdf

http://www.quantonline.co.za/documents/Generating%20South%20African%20Volatility%20Surface.pdf

The route change via Sea Point was really appreciated (versus Mordor).

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