What would I make or lose on this options trade, and where does it break even?
Buy a call option: gains when the stock rises, loss limited to the premium
| Greek | Value | Interpretation |
|---|---|---|
| Delta | 0.523 | Position change per $1 stock move, per share |
| Gamma | 0.0555 | Rate of change of delta |
| Theta | -0.05 | Position change per day of time decay, per share |
| Vega | 0.11 | Sensitivity to 1% volatility change |
| Rho | 0.04 | Sensitivity to 1% interest rate change |
Unlimited (stock price - strike price - premium)
Premium paid
A long option can expire worthless, so the whole premium is lost. Selling options can lose far more than the premium collected. US stock options are American style and Black-Scholes prices European options, so the premium here is an estimate. Brokers require approval to trade options.
Key greeks:
How options behave:
Start with a $100 stock, a $100 strike, 30 days to expiration, 25% volatility, a 4.1% risk-free rate, and a 2% dividend yield. Black-Scholes prices the call at $2.94 a share and the put at $2.77. One contract covers 100 shares, so buying the call costs $293.85. That is also the most you can lose. The break-even price is $102.94, and the stock has to close above it at expiration for the trade to profit. The model puts the chance of that at 33.88%. If the stock finishes exactly at $100, the call expires worthless and the result is a $293.85 loss. Delta is 0.523 per share, so a $1 rise in the stock moves the position about $0.52 per share, and theta of -0.050 means about $5.02 a day in time decay on the contract. Switch to a bull call spread with a $105 second strike and the cost drops to $1.81 a share, the break-even to $101.81, and the most you can make is capped at $3.19 a share.
Finance Quest is educational. It is not financial advice, and no calculator here knows your full situation.
A strategy with a large or unlimited upside draws the eye, and the long call in the example does have no cap on profit. But the same run shows a 33.88% chance of finishing in profit and a certain loss of the full $293.85 if the stock goes nowhere. A covered call at the same inputs reverses the picture: a 65.70% chance of profit, but the gain is capped at the $2.94 premium a share. Check max profit, max loss, break-even, and probability of profit together, since each one alone tells half the story.
At expiration, add up what each leg is worth at the final stock price, then subtract the premium you paid or add the premium you received. For a long call that is the stock price minus the strike (never below zero), minus the premium. Multiply by 100 for one contract.
It is the stock price at expiration where the trade makes no profit and no loss. For a long call it is the strike plus the premium; for a long put it is the strike minus the premium. In the lab's starting numbers, that is $102.94 for the call and $97.23 for the put.
It is the share of Black-Scholes outcomes in which the position finishes above zero at expiration, using the volatility you entered. It is a model output, not a forecast, and it changes whenever volatility, days to expiration, or the premium changes.
The lab prices with Black-Scholes from the inputs you give it. Market prices reflect supply, demand, and the volatility traders actually expect. Type the broker's premium into the premium field and the profit, loss, and break-even recalculate from it.
Eight: long call, long put, covered call, cash-secured put, bull call spread, bear put spread, iron condor, and long straddle. Each shows the same set of outputs so you can compare them on the same stock.
The lesson for this lab is in Chapter 13, Stock Market Basics. Read the lesson