Everything in the last two modules priced an option on its own. This lesson is about what happens when you put a stock, a call and a put together at the same strike and the same expiration. The market risk cancels, and what is left is a small, fixed amount of money. That amount is how market makers earn their keep, and it is why the call and put prices on any chain are tied to each other by interest rates and dividends.
The conversion
Buy 100 shares, sell one call and buy one put, both at the same strike and expiration. Call the strike K. At expiration one of two things happens. If the stock is above K, your short call is assigned and you deliver the shares for K. If it is below K, you exercise your put and sell the shares for K. Either way you end up with exactly K in cash. There is no outcome where you keep the stock or where the price matters.
So a conversion is a position that turns into K dollars on a known date. What it costs today is the stock price, minus the call price, plus the put price. Say the stock is $200, the $200 call is $6.20 and the $200 put is $5.50. You pay $200, collect $6.20 and pay $5.50, so $199.30 all in. At expiration you get $200. That is a locked-in gain of $0.70 on $199.30 over the life of the trade.
That $0.70 is not free money. It is the interest you could have earned on the strike, less any dividend the stock pays before expiration. If the trade runs 45 days at a 4% rate, the interest on $200 is about $0.99. If a $0.30 dividend goes ex before expiration, the holder of the stock collects it, which brings the fair gap down to about $0.69. The market priced the call and put so that the conversion earns almost exactly its cost of holding the stock, called the carry. Count the dividend you collect as the stockholder and the total comes back to about $1.00, the interest. That is the whole point: a conversion is a way of lending cash, and it pays what lending pays.
Long 100 shares at $100, short the $100 call, long the $100 put, entered with 60 days left. The P&L at expiry is a flat line: the interest on the strike. Drag the rate to 0% and the line drops to zero; pull the days down to watch the gain build.
Every leg that gains when the stock moves is matched by one that loses the same amount, so all that is left is the gap between what you paid and the strike you are sure to receive. Cut the rate to zero and the conversion earns nothing, because cash earns nothing.
The reversal
A reversal is the mirror image: sell the stock short, buy the call and sell the put. You take in a little less than the strike today and pay the strike back at expiration, when you buy the shares back through one option or the other. It is borrowing. It is fairly priced when the gap you give up equals the interest on that cash minus the dividends you owe on the short stock, so a reversal and a conversion sit at the same price and neither side has an edge.
Short the stock at $100, long the $100 call, short the $100 put. The entry note shows the credit you take in; the flat loss at expiry is the interest on that cash. Raise the rate and the cost of this loan rises with it.
The flat loss is not a trading loss. You took in a little less than the strike and pay the full strike back, so the loss is the interest on that loan. When a stock is hard to borrow, the short seller also pays a fee, and it shows up on the chain as puts that look expensive against the calls.
How market makers use them
A market maker who sells a customer a call does not want the stock risk. The first move is to buy shares against it, the delta hedge from Module 6. The second move is to buy the put at the same strike. Now the maker holds a conversion: no delta, no gamma, no vega, only carry. The position sits until expiration, or until someone wants the other side. Conversions and reversals are how the options market lays off risk and finances itself, and every quote on the chain assumes they are available.
What the gap tells you
Because the conversion must earn the carry, the call minus the put at any strike, less the stock price minus the strike, equals the interest minus the dividend. Read it off the chain and you have the market's own view of the rate and the dividends to that date, without looking either up. A gap that is clearly positive means interest is winning. A gap near zero or below usually means a dividend falls before expiration that is about as big as the interest, or bigger. Put-call parity from Module 2 is this same statement in equation form; the conversion is the trade that enforces it.
If the call were bid up a dollar over fair value, a market maker would sell it, buy the put and buy the stock: a conversion earning the carry plus a dollar, with no risk. That trade runs until the dollar is gone, which is why a call and a put at one strike never drift apart.
Call minus put at the $100 strike against the stock price. Every line is straight, like stock. At expiry it is the stock price minus $100; before expiry it sits higher, by the interest on the strike. Raise the dividend yield and the lines sink below the expiry line.
A long call and a short put at the same strike behave like agreeing to buy the stock at the strike on the expiration date, a position called a synthetic forward. Its price, the strike plus the call minus the put, sits above the stock price by the interest and below it by any dividend, because the forward owner keeps their cash earning interest but never collects the dividend.
The maths: parity with interest and dividends
For European options at strike K with T years to expiration: C - P = S - PV(D) - K e^(-rT). Here C and P are the call and put prices, S is the stock price, r is the interest rate, K e^(-rT) is the strike's present value (what you would set aside today to have K on the expiration date), and PV(D) is the present value of the dividends that go ex before expiration.
Worked example: stock and strike both $100, three months left, a 4% rate and one $0.50 dividend before expiration. K e^(-rT) = 100 × e^(-0.01) = 99.005. So C - P = 100 - 0.50 - 99.005 = 0.495: the call is worth about 50 cents more than the put. With no dividend it would be 99.5 cents. The conversion costs S - C + P = 100 - 0.495 = 99.505 and returns the $100 strike plus the $0.50 dividend, $100.50. The gain is $0.995, which is 4% on $99.005 for a quarter of a year, the rate and nothing more.
US stock options are American, so on the chain this holds only approximately; for at-the-money options with a few weeks left the difference is too small to see.
Your turn
Open the MSFT chain on the next monthly expiration, find the at-the-money row and read the call mid and the put mid. Then work out the synthetic forward and the parity gap, and decide whether interest or dividends are winning on that date.