Every option is priced against a date in the future, not against today. The price the market uses for that date is the forward price: what it costs to lock in the stock now for delivery then. On most chains the forward sits a little above the stock price, and once you know why, half of the next three lessons is already done.
Two ways to own a stock in six months
Say a stock trades at $200 and you want to hold it in six months. You have two routes. Route one: buy it today for $200. Your cash is tied up, so you give up the interest it would have earned, but you collect any dividend the company pays along the way. Route two: agree today to buy it in six months at a fixed price, and keep your $200 earning interest in the meantime. That fixed price is the forward, and it has to be set so that neither route is a free lunch.
Put numbers on it. Interest rates are 4% a year, so $200 earns $200 x 0.04 x 0.5 = $4 over half a year. The stock yields 1% a year in dividends, so a holder collects $200 x 0.01 x 0.5 = $1 in that time. The forward is $200 + $4 - $1 = $203. Interest pushes it up, dividends pull it down, and the net $3 is called the cost of carry. The exact formula compounds the rate, but for a few months the straight-line version lands within pennies.
Why it has to be that price
Suppose the six-month forward were $206. You would borrow $200, buy the stock and agree to deliver it at $206. You owe $4 of interest and collect $1 of dividend, so the stock costs $203 all in: $3 with no risk. At $200 you would do the reverse, shorting the stock and banking the cash. These trades are called cash-and-carry and reverse cash-and-carry, and they need no view on the stock, which is why the forward cannot stray far from spot plus carry.
Which way it leans
- Rates above the dividend yield: the forward sits above spot. This is the normal case for most stocks and for the index.
- A high-yield stock when rates are low: the forward can sit below spot.
- Only dividends paid before expiration count. If the expiration falls before the next ex-dividend date, that chain's forward carries no dividend at all, and it steps down for the first expiration after the ex-date.
- Stock that is expensive to borrow behaves like a stock with a bigger dividend, so its forward sits lower.
Carry moves every option on the chain
Options are priced off the forward, not off spot. A call is a claim on the stock above the strike at expiration, so when the forward rises the call is worth more and the put is worth less, even though the stock has not moved. That is why a higher interest rate lifts every call and lowers every put, and a bigger dividend does the opposite. Carry is charged per year, so the effect is small on a one-month option and grows with time.
A $100 strike at 30% volatility with 180 and 30 days left. Drag the interest rate up and the call lines rise while the put lines (switch to Put) fall; drag the dividend yield up and they move the other way. The 180-day line moves far more than the 30-day one.
Six months out, moving the rate from 0% to 8% is worth about $2 on a $100 at-the-money option, up for the call and down for the put. One month out, the same move is worth about a third of a dollar.
Not a forecast
The forward drifting higher with time says nothing about where the market thinks the stock is going. It is the cost of money, nothing more. A forward $3 above spot is not a bullish signal, and a trader who reads it as one will misjudge every call and put on the chain.
The chain already knows the forward
You never have to look up the rate or the dividend schedule. Options price the forward directly: at any strike, the strike plus the call price minus the put price equals the forward, give or take a few cents of discounting. At the one strike where the call and the put are worth the same, that strike is the forward. The next lesson shows why. For now, use it as a tool: find the strike where the two mids match, and you have read the forward straight off the chain.
The chart runs that idea on a made-up $100 stock: buy the six-month $100 call, sell the $100 put, and the package breaks even at $100 plus what you paid, which is the forward.
Long the $100 call and short the $100 put, six months out, at a 4% rate and a 1% dividend yield. The breakeven marker sits near $101.50, the six-month forward. Drag the rate or the dividend and watch it follow the carry.
The maths: the forward price formula
With continuous compounding the forward is F = S × e^((r - q) × T). S is spot, r the interest rate per year, q the dividend yield per year, T the time to delivery in years, and e the base of natural logarithms, about 2.718. The term (r - q) × T is the cost of carry for the period.
Worked example: S = $200, r = 4%, q = 1%, T = 0.5. Then (r - q) × T = 0.03 × 0.5 = 0.015, e^0.015 is about 1.01511, and F = 200 × 1.01511 = $203.02. The straight-line version in the text gave $203.00; compounding adds two cents over six months.
Real dividends arrive as lumps, not as a smooth yield. For a single stock the exact version subtracts the present value of each dividend paid before expiration: F = (S - PV(dividends)) × e^(rT). The chain arithmetic, strike plus call minus put, also skips a small discount factor: the exact form is F = K + (C - P) × e^(rT), a cent or two different when the strike is near the money.
Your turn
Open SPY in the Terminal. Read the price from the quote bar, then open an expiration about six months out and work out the forward from the at-the-money strike. Finish with MSFT's dividend yield on the Dividend Analytics panel.