Outofpriceoption

outofpriceoption

This is not a joke. For example, Vega is the first derivative of a derivative contract an option value with respect to volatility.

Dies ist vor allem bei langen Laufzeiten vorteilhaft, da hier der erwartete exponentielle Anstieg des Kurses berücksichtigt werden kann.

To calculate the offer price, we use 7. Vega is 2, EUR, outofpriceoption consequently, if volatility rises to 8. Note that the mathematical Vega in the sense of a pure derivative of the Black-Scholes formula with respect to volatility is 0.

outofpriceoption

Homework question: how does this relate to a Vega of EUR 2, that a trading system shows? And obviously for the Newton fans this captures outofpriceoption the linear part of the impact of changing volatility.

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Now, we all know that a single volatility is no sufficient for valuation of vanilla options, but rather a volatility surface is required, which captures both smile and term structure.

Therefore, when we want to quantify the impact of the change of the volatility surface on the value of the derivative contract, one common way is to use the key input values for the construction of the volatility surface. Revga and Bufga turn out to outofpriceoption zero, so rather boring.

outofpriceoption

This is because the option is ATM, whence the smile will have no impact on the value as long as the ATM-volatility stays outofpriceoption same. The offer price may then be EUR 10, Outofpriceoption change of the Risk Reversal from Similarly, raising the Butterfly from 0.

Note that these figures here depend on the model we use to price the RKO.

outofpriceoption

Depending on your model choice, you may see slightly different figures. Here is a job for the weekend: how can we approximate Revga for a Delta Risk Reversal? Assuming zero interest rates, the rule of thumb is about 32 basis points of the EUR notional multiplied outofpriceoption the square root of time outofpriceoption maturity, e.

Outofpriceoption knowing the Revga of any derivative contract, a trader can quickly determine by the rule of three how many Risk Reversals are required for hedging.

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We illustrate its relationship to Revga for a plain vanilla call in Figure 1. The figure shows that both Greeks are related to the skew, which is why both are zero near the ATM strike.

outofpriceoption

outofpriceoption Figure 1: Revga and Vanna of a 6M vanilla call on the strike space x-axis on a 1. Vanna and Volga do not take the smile information into account at all; they are just simply second order model Greeks. The reason why they look similar in the graph is that a vanilla option is most sensitive to Risk Reversal changes near the point where Vanna peaks, and with a suitable scaling factor one might think they are generally roughly the same.

outofpriceoption

Uwe Wystup.

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