Vega and rho

Delta, gamma and theta deal with the stock price and the calendar. Vega deals with the market's changing opinion about how much the stock will move, and it is the Greek that most often ambushes traders who thought they had a directional trade. Rho deals with interest rates and is, for most retail positions, a footnote worth knowing.

Vega

Vega is the change in the option's price for a one-percentage-point change in implied volatility. (Implied volatility is defined properly in Module 4; for now, it is the market's expected annualised movement in the stock, quoted as a percentage.)

XYZ at $50, the 30-day $50 call trades at $1.90 with implied volatility 32% and vega 0.057. If implied volatility rises to 35%, three points, the call should rise by about 3 × $0.057 = $0.17 to $2.07 with XYZ unchanged. If it falls to 25%, seven points, the call drops about $0.40 to $1.50.

Long options (calls and puts alike) have positive vega: they gain when implied volatility rises. Short options have negative vega.

Vega across strikes and time

Vega, like theta and gamma, is largest at the money. Unlike gamma and theta, it is largest for long-dated options, because a change in expected volatility matters more when there is a long time for it to play out.

A one-year ATM option moves about $0.20 for each volatility point, seven times as much as a one-week option. That has two consequences:

• Long-dated options are volatility positions as much as directional ones. If you buy a LEAPS call when implied volatility is high, a return to normal volatility can cost you more than a mild adverse move in the stock.
• Short-dated options are relatively insensitive to volatility and dominated by gamma and theta. That is one reason very short-dated selling is popular, and one reason it is dangerous: the Greek that is small is the one that would have warned you.

Vega in a worked trade

You buy the 90-day $50 call for $3.30 with implied volatility at 40%, because XYZ has been moving a lot and you expect the move to continue. Vega is 0.099. Over the next three weeks XYZ drifts up $1.50 to $51.50, but the market calms down and implied volatility falls to 28%.

• Delta gain: roughly +0.55 × $1.50 = +$0.83.
• Theta over 21 days: roughly −$0.45.
• Vega loss: 12 points × $0.099 = −$1.19.
• Net: about −$0.81 per share, an $81 loss per contract on a trade where the stock went up.

The volatility drop cost more than the stock move earned. Module 5 lists this as one of the three ways to lose while being right about direction, and Module 4 shows how to check implied volatility before buying so it does not happen to you.

Key idea: Vega is your exposure to the market changing its mind about how much the stock will move. It is largest at the money and in long-dated options, and it can override direction entirely.

Rho

Rho is the change in option price for a one-percentage-point change in the risk-free interest rate. Calls have positive rho (higher rates make the strike's present value smaller, which makes the right to buy at that strike more valuable); puts have negative rho.

For short-dated options rho is tiny. A 30-day ATM option on a $50 stock has rho around 0.02, so even a full percentage point change in rates, which happens over months not days, moves the option by two cents.

For long-dated options it matters. A one-year ATM call on a $100 stock has rho around 0.45: a one-point rate move is worth $0.45 per share. The main practical effects:

• LEAPS calls are noticeably more expensive when rates are high, and LEAPS puts cheaper, because the call embeds the interest you save by not buying the stock outright.
• Put-call parity's interest term (Module 2) is rho at work: it is why the call and put at the same strike can differ by several dollars a year out.
• Deep ITM puts can be worth exercising early when rates are high, because the cash from selling the stock can earn interest now rather than at expiration. Module 7 touches on this.

Unless you trade LEAPS or you are in a period of fast rate changes, rho is the Greek you check once and then ignore.

Reading a Greeks panel

Put together, a typical display for our 30-day $50 call:

That row is the whole position, described. Before any option trade, read the row and ask what each number means for the scenarios you actually expect.

Try it: Find a stock with an earnings date in the next month. Compare the vega of the option expiring just after earnings to the one expiring two months later. Then estimate what a 15-point drop in implied volatility after the announcement would do to each. Module 4 will show you why that drop is nearly guaranteed.

Recap

• Vega is price change per one-point move in implied volatility; long options have positive vega, short options negative.
• Vega is largest at the money and grows with time to expiration; long-dated options are largely volatility bets.
• A drop in implied volatility can wipe out a correct directional call; check IV before buying.
• Rho measures interest-rate sensitivity; it is negligible short-dated and meaningful for LEAPS.
• Read the full Greeks row before trading and translate each number into a dollar scenario.