Which of the following is NOT one of the assumptions of the Black-Scholes-Merton option-pricing model? A) There are no taxes and transactions costs are zero for options and arbitrage portfolios. B) There are no cash flows over the term of the options. C) The yield curve for risk-free assets is fixed over the term of the option. Your answer: C was correct! The yield curve is assumed to be flat so that the risk-free rate of interest is known and constant over the term of the option. Having a fixed yield curve does not necessarily imply that the yield curve is flat. My question is really unrelated to the problem–it is what is the difference between a fixed and flat yield curve. I cannot even find the definition of a fixed yield curve online.
fixed= constant, i.e. doesn’t change
how is flat any different? black scholes formula assumes rfr is constant and known.
the risk-neutrality in the black scholes formula is based on the assumption that you can replicate the derivative payoff by creating a portfolio of the underlying stock and borrowed cash at the risk-free rate. as the stock price moves, you dynamically change your position in the stock and the amount of cash in the portfolio. you borrow at the short-term interest rate. if the yield curve is not flat, the forward short-term interest rates will be different at any point in the future. by assuming a flat yield curve, you are saying that the short-term interest rate remains constant. if the yield curve is fixed, but not flat, that just means that (theoretically) all of the forward short-term rates are known, but they are not constant.
you could have a normal yield curve (lower rates at the short end–2, 3, 5 years, and higher rates at the long end–10, 30 years). A flat yield curve means that interest rates are the same at every maturity (i.e. the 2 year rate is the same as the 30 year rate). BS assumes that rates don’t change over the life of the option, meaning that the yield curve is flat.
tenten Wrote: ------------------------------------------------------- > how is flat any different? > > black scholes formula assumes rfr is constant and > known. flat is flat…if your a level II candidate you should have a solid understanding of a yield curve. Don’t mean to come off as rude, but this is absolutely basic stuff.
That couldn’t have sounded more rude. Your explanation does make a flat and fixed yield curve sound the same… Since you couldn’t reason the subtle difference you obviously dont know either.
chedges Wrote: ------------------------------------------------------- > That couldn’t have sounded more rude. > > Your explanation does make a flat and fixed yield > curve sound the same… Since you couldn’t > reason the subtle difference you obviously dont > know either. Yes, I have no idea what a flat yield curve is vs. a fixed constant yield curve. Oh man, I might just end up losing my job as a fixed income trader, please bestow your godly knowledge on me chedge 
Fixed: The yield curve could be normal or inverted or flat but remains the same during the tenure in consideration… Flat: where LT rates = ST rates