The investor fears a sharp decrease in the share price so the investor should buy a put option. This will act as a hedge against a potential drop in price. LG is a dividend paying company so an American put option will be better because with a dividend paying stock, it can happen that early exercise will be more profitable that waiting till the expiry of the option. This happens because depending on when the dividend is to be paid, stock prices usually fall by the dividend amount on the ex-dividend date. This increases the payoff from the put option as the payoff is strike price less the stock price.
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