could anyone outline the inter-relationships between theta and vega and between vega and delta ? is there a way to graphically describe those relationships (e.g how vega changes with time), or put numbers on them? thnks/
For single options, VEGA and THETA have opposite signs. THETA is also basically the inverse of GAMMA so, positive VEGA comes along with positive GAMMA and negative THETA. As time passes VEGA magnitude declines and at the same time GAMMA/THETA magnitude increases. For simplification purposes, you may want to think of it as somewhat of a linear relationship. VEGA, GAMMA and THETA peak i.e. have their highest magnitude for ATM options. DELTA on the other hand tends to 1 for ITM options and tends to 0 for OTM options. So, for the DELTA/VEGA relationship, VEGA is highest for DELTA .50 options and lowest for DELTA 1 and DELTA 0 options etc. As time passes, VEGA decreases as discussed and there is also DELTA drift. Pick up a decent book with graphs of the greeks e.g. Option Volatility & Pricing or Options Trading: The Hidden Reality (has 3d graphs you may find useful). In fact, most introductory texts that cover the greeks have some kind of graphs. However, AFAIK most graphs in books will show greeks with respect to time, moneyness (price) and IV and not greeks vs. greeks which is what you are asking. Perhaps what you were really asking is THETA and DELTA versus IV which is not the same as THETA and DELTA versus VEGA. You can also plot your own graphs in Excel etc. if you want, using a tool such as: Hoadley's Option Strategy Analysis Tools Some random online URLs: Volatility and the Greeks from 888options.com Some 3D graphs of greeks with respect to time and price Good luck. MoMoney.