The original Black-Scholes model is based on many assumptions; Assumptions about the market in the BS model are: 1) There are no arbitrage opportunities. 2) It is possible to borrow and lend any amount of cash at the same rate as the interest rate of the risk-free asset. 3) It is possible to buy and sell any amount of stock (including short selling). 4) There are no transaction costs in the market. What's a real life example of #2 and #3? When market-makers sell/buy options on a stock and make a market, where do they find they money and shares to hedge? What is a real-life example of #2 in action? And as far as #4 goes.. there are obviously transaction costs for the dynamic hedger/market maker (clearing fees, exchange fees). Is the cost of the hedge is embedded in the price of the option? If so, where does their profit come from if the price of the option is the cost of dynamically hedging?
"What's a real life example of #2 and #3?" #2 - Only if the Central Bank trades options. For anyone else, this does not exist. For large traders it is absolutely essential to work in a place with a very strong balance sheet that affords the lowest rate possible and the narrowest bid/offer between borrowing and lending rates. #3 - Just a model assumption, you probably can buy/sell any amount of stock, but not for one price. #4 - Cost of hedging is embedded in the price of the model. That cost is also assumed to be 0. Any cost beyond that (reality) is not modeled into the model. The cost of the option is determined assuming dynamic hedging at a cost of zero. It's just a math thing. If one were to never hedge it changes 0 the value of that option. I dynamically hedged, you won't. That option is worth the same to both of us. Theoretically our outcomes should be the same respecting the law of big numbers.