R27, page 112 (2020)
It says you can synthetically replicate a call option by going long the convertible bond and short the stock.
Because you are short the stock don’t you lock in your gains? I can’t seem to get around what kind of payoff that resembles a call option payoff.
Greetings friend! It seems like they are referring to convertible bond arbitrage, correct? I don’t have the reading in front of me, but what you’re describing seems like this.
In convertible bond arbitrage, the premise is that a trader separates the convertible bond into 2 components: the straight bond and the equity call option component. The analyst has diligently reviewed the convertible bond price and the current stock price, and sees that the convertible bond (consisting of the 2 components above) is priced at a level that undervalues (or overvalues) the equity call option component of the convertible bond if it’s exercised (i.e., you can get stock from exercising the conversion option on the convertible bond more cheaply than buying it straight from the stock market). You then take a position to try to arbitrage on this through careful delta hedging.
Let’s for simplicity’s sake say the equity call option on the convertible bond is undervalued. If you use the correct delta hedging ratio, you can short the stock and go long the convertible bond to synthetically mimic a call option of sorts, because if the stock goes up you make the difference in the undervalue amount of the call option component of the convertible bond. Your net gains will be the amount of extra value you get above the short stock, and it will vary as the call option moves more and more into moneyness. If the stock goes down on the other hand, the gains from your short stock position should neutralize your losses in the convertible bond value. So it ends up looking like a call option (limited downside, positive upside that changes with price movement).
Does this help? If there is a jedi options trader or convertible arbitrageur here who can explain it better, I defer to their feedback of course. I am just a standard level trader who’s just trading for fun these days. But this is my understanding above, for what it’s worth.
Cheers - good luck - you got this 