Forward conversion with options - European/American options?

The title says it all.

If I used American options, wouldn’t the shares be called by the call buyer the instant it goes above strike price? If so, it wouldn’t be accurate to say that the purchase of put and sale of call at the same strike price and same expiry creates a riskless position.

I suppose this would work only if we used European options.

I think it is European options.

In my experience, options usually stay in the account even if it’s deep in the money. The only times they get called was when there was a dividend payment coming up and the call options are already deep in-the-money. The price movement from the dividend payout would very unlikely drop below the strike price.

I confirm. Even though American options can be exercised at any time, investors rarely exercise before maturity. The is because the option price will remain higher than the intrinsic value unless you are very close, so instead of exercising, they just sell their options.

For ex: I sold 100 Calls on XOM strike 80, 6m to expiry. Spot = 85, current option price = $7

It would not make sense for the buyer to exercise his calls because he would only make $5 (minus premium paid) vs. 7 if he sold the options; the only reason he would exercise now would be if a dividend of \>= 2 will be distributed soon.