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  1. Is there a difference in the value of Delta of American and European options with the same underlying asset price, strike price, time to maturity?

  2. Also, is there any way to determine the price of an European call option using Black Scholes Formula, while only being given the strike price, volatility, risk free, time to maturity and dividend yield, with the underlying asset price being unknown?

Current stock price: Unknown

Strike Price (K): $41.50

Volatility: 30%

risk-free: 10.22%

Time to maturity: 3-months

Dividend yield: 0 (non-dividend paying stock)

Or can the underlying asset price be calculated in another manner?

Thanks!

  • 1
    Q2: You can't solve a single equation with two unknown variables though you could iterate one variable and come up the other for each increment of additional underlying price (as done with determining implied volatility). – Bob Baerker Mar 12 at 12:03
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Is there a difference in the value of Delta of American and European options with the same underlying asset price, strike price, time to maturity?

Probably. The difference between American and European options primarily affects the expiration date - American have multiple expiration dates while European have one. As a result a different method is used to price American options than Black Scholes. A deeply in-the-money or far out-of-the-money option with a delta of 1 or 0 respectively will have the same value, or an option that expires in one day.

is there any way to determine the price of an European call option using Black Scholes Formula, while only being given the strike price, volatility, risk free, time to maturity and dividend yield, with the underlying asset price being unknown?

The price of the underlying asset is a required variable to calculate the price of the option. You could algebraically simplify the Black Scholes equation to a formula for the price of the option once you are given the price of the underlying asset based on the supplied parameters. If you don't have the underlying asset price, it is impossible to tell whether or not the option is in-the-money, at-the-money or out-of-the-money and by how much (this comes from the difference between the underlying asset price and the strike price).

  • The way that the second part of your answer is normally done in practice is by employing a Monte Carlo simulation FYI. OK it's not strictly the price of the underlying that is modelled but close enough – MD-Tech Jun 12 at 16:06
  • @MD-Tech My understanding is that MC is used for large portfolios of OTC stuff that is otherwise difficult to price, as MC is incredibly inefficient from a CPU or compute standpoint. Other methods are more effective for single stock options. Yes, other factors than just price are also taken into account. – xirt Jun 12 at 16:17
  • MC is much cheaper these days with cloud computing etc. but it depends on the underlying (it is used more for FI underlyings) and the use of the price. Also remember that the tree methods you see in many quant books for pricing American bonds is essentially an MC method. In reality the MC is used to model volatility since you normally know the current price of an underlying from BBG – MD-Tech Jun 12 at 19:44

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