Higher Order Greeks:

Vanna, Volga and Charm

Oleg Mubarakshin, ITinvest

Moscow Option Conference

2016-04-09

R Project

Vanna

\[ \text{Vanna} = \frac{\partial \text{Delta}}{\partial \text{Vol}} \equiv \frac{\partial \text{Vega}}{\partial \text{Spot}}\]

Vanna of Calls

ATM Call

OTM Call

ITM Call

Vanna of Puts

ATM Put

OTM Put

ITM Put

Cost of Vanna

Portfolio: Risk Reversal

type strike quant vol delta vega theta gamma vanna
Call 108 -1000 21.9 -256.8 -160.0 19.5 -29.6 -11.2
Put 94 1000 19.0 -240.8 154.7 -16.3 33.0 -10.0
Fut 0 498 0.0 498.0 0.0 0.0 0.0 0.0
Sum 0 0 0.0 0.4 -5.4 3.2 3.4 -21.2

Risk Reversal: P&L

Risk Reversal: Delta

Risk Reversal: Vega

Risk Reversal: Vanna

Risk Reversal: Delta(Vol)

Volga - Vomma - Vega convexity

\[ \text{Volga} = \frac{\partial \text{Vega}}{\partial \text{Vol}} \equiv \frac{\partial^{2}\text{V}}{\partial \text{Vol}^2}\]

ATM & OTM Options Volga

Cost of Volga

Portfolio: Fly

type strike quant vol delta vega theta gamma volga
Put 91 -800 18.6 114.6 -89.8 9.3 -19.6 -5.0
Call 100 1000 20.0 519.8 197.9 -22.0 40.1 0.0
Call 114 -800 23.6 -116.2 -90.6 11.9 -15.5 -4.8
Fut 0 -518 0.0 -518.0 0.0 0.0 0.0 0.0
Sum 0 0 0.0 0.2 17.4 -0.8 5.0 -9.8

Fly: P&L

Fly: Vega

Fly: Volga

Fly: P&L(Vol)

Charm - Delta Decay

\[ \text{Charm} = -\frac{\partial \text{Delta}}{\partial \text{Time}} \equiv \frac{\partial\text{Theta}}{\partial \text{Spot}}\]

Delta Decay Risk

Self-hegding of Delta Decay:

  • Strangles
  • Straddles

High level of Delta Decay:

  • Delta-hedged Calls
  • Delta-hedged Puts
  • Risk reversals

Thank you!

Contacts

ITinvest’s Derivatives Desk

+7 (495) 933-32-32 (ext. 2559)

This presentation is available on

http://quant-lab.com