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The Black-Scholes/Merton equation [video]

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Re: The Black-Scholes/Merton equation [video]

#3

Post by JumpCrisscross »

mhh__ wrote: post #2

Black-scholes is a hedging argument, the eqn isn't the essence of it

Eh, put-call parity is the hedging argument [1]. Black-Scholes-(Merton) was a breakthrough because it lets one understand why the hedge works, and thereby hedge and price more precisely.

[1] https://en.m.wikipedia.org/wiki/Put–call_parity

Re: The Black-Scholes/Merton equation [video]

#6

Post by sixers2329 »

JumpCrisscross wrote: post #3
mhh__ wrote: post #2

Black-scholes is a hedging argument, the eqn isn't the essence of it

Eh, put-call parity is the hedging argument [1]. Black-Scholes-(Merton) was a breakthrough because it lets one understand why the hedge works, and thereby hedge and price more precisely. [1] https://en.m.wikipedia.org/wiki/Put–call_parity

What I never fully understood is there’s a free parameter in the equation (Implied Volatility)- which has no solid definition besides “the number that makes the rest of the equation work”. At that point… how much value are you really getting from the rest of the equation?

Re: The Black-Scholes/Merton equation [video]

#8

Post by lordnacho »

sixers2329 wrote: post #6
JumpCrisscross wrote: post #3

Earlier quoted context omitted.

Eh, put-call parity is the hedging argument [1]. Black-Scholes-(Merton) was a breakthrough because it lets one understand why the hedge works, and thereby hedge and price more precisely. [1] https://en.m.wikipedia.org/wiki/Put–call_parity

What I never fully understood is there’s a free parameter in the equation (Implied Volatility)- which has no solid definition besides “the number that makes the rest of the equation work”. At that point… how much value are you really getting from the rest of the equation?

Former option trader here. The free parameter is actually the "thing" that you're actually trading when you trade an option. All the other parameters are just environmental, you look them up.

The short story is that the implied vol is a sort of balancing price between how much the option loses in value over time vs how much you can make performing the hedge.

Re: The Black-Scholes/Merton equation [video]

#9

Post by scherlock »

sixers2329 wrote: post #6
JumpCrisscross wrote: post #3

Earlier quoted context omitted.

Eh, put-call parity is the hedging argument [1]. Black-Scholes-(Merton) was a breakthrough because it lets one understand why the hedge works, and thereby hedge and price more precisely. [1] https://en.m.wikipedia.org/wiki/Put–call_parity

What I never fully understood is there’s a free parameter in the equation (Implied Volatility)- which has no solid definition besides “the number that makes the rest of the equation work”. At that point… how much value are you really getting from the rest of the equation?

Implied volatility is really the standard deviation of the price over time. You can calculate it by look at prices in the market. Then interpolate values. Where banks get funky is that the market for options go out about 3 years, but a banks will write options going out much much further. For those options, they are really just guessing, no matter how much fancy math they do, it's all to dress up a guess. And the traders don't care since they won't be around when the option expires
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