Option theta (FRM T4-18)

[@kaiwang2924]

I like how you put all the most valuable information into one single graph.

[@millamulisha]

Have been looking forward to more of these videos on the Greeks. Thanks! So informative.

[@易哲源]

Thanks for providing the Greece letter graphs. Those illustrations really make sense and help understand how each letter varied with stock price(S), strike price(K), DTE, volatility, and risk-free rate.

[@易哲源]

Need to point out American options will never have POSITIVE Theta.

[@hit3212]

One of the best explanations of option greeks!

[@commonmancrypto1648]

Theta radiation melts diamond hands. Great video.

[@dompatrick8114]

You break these down so nicely. Thanks.

[@zavainmardirossian8593]

Hi, could you please give an example how to use the formula say for call option in substitution of real live figures. I.e a real example please.

[@adamgora1]

Are you sure theta has negative value? When time to expiry goes down then option value goes down therefore partial derivitve is positive. It is the same analogy as for delta of an option, or am I wrong? Great videos.

[@bionicturtle]

Excellent observation! If you notice #1 in the initial list (kzbin.info/www/bejne/gGnWaGaNqJ1knNk) I show Θ = -∂c/∂T; i.e., there is a negative sign in front of the pure partial derivative. As you say, option value increases with maturity such that 1st derivative is mathematically positive. However, we experience time decay (going forward in time) as a decreasing time to expiration, hence the negation. Apologies if I wasn't super-clear about that because it is convention to say (and graph) "theta is negative" to reflect the implication that time decay reduces option value. With respect to delta, I do not perceive an analog: delta is the pure 1st derivative without even infection by a sign (+/-). A good analogy actually would be bond (dollar) duration: the first derivative of bond price with respect to yield is mathematically negative, but by convention it is negated so that (eg) duration of 5.0 years refers to an increase of 1.0% yield that approximates a decrease of 5.0% in bond price. (the first derivative is actually negated and divided by price, such that modified duration = -1/P * ∂P/∂y, so even this analogy is strained). I hope that's helpful, thank you for a smart observation!

[@ihsanatlitv]

this course is for a retail trader or market makers?

[@arturoaramburo9365]

Are the Greeks for American options different? Thank you..

[@dedicatedmotion1960]

Greeks are just as the European Greeks the only difference is that theta is divided by 365 and Vega and Rho are divided by 100

[@anindadatta164]

Positive theta in two exception cases not clear. If a company declares high dividend resulting in fall in underlying share price, then the resulting increase in call option premium should be attributable to delta and not theta. Also how could a deep in money put option have positive theta.? Also, the two graphs of call option theta depicted in the video show all theta values to be negative.

[@bionicturtle]

Nice try but ... I think all of your points are incorrect, sorry. These are European options. A deeply ITM European put can have positive theta because more time gives volatility a chance to kick the option into less/no value, yet there is limited further upside (volatility is not symmetrical for the call and the put, the call has unlimited upside but the put is bounded). Imagine you have an extremely deeply ITM put option, the S(0) is near zero: you would exercise immediately if you could! Unlike "normal" options, you want less time not more. Yes, the two graphs are for call options on non-dividend paying stocks per the displayed inputs.The exceptions are deeply ITM put and deeply ITM call with high dividend yield. Notice the theta graph for puts does show positive theta for the ITM option (green line)

[@anindadatta164]

I tested the put option theta equation with different data sets , and in all cases I took K=3S or K=4S , indicating deep in money put option.,. However, every time theta was negative value

[@bionicturtle]

It sounds like your formula is incorrect. My xls can be downloaded and my theta is tested (i.e., i show in the video an example where it correctly approximates the repriced difference). In my XLS, for the assumptions given, theta for my 1-year put breaks from negative to positive at only S(0) = $73.17 while K = $100.00. In fact, you can see from the formula, the bound occurs at exactly where S(0)*N'(d1)σ/(2*sqrt(T)) = r*K*exp(-rT)*N(-d2); both of these terms are positive.

[@anindadatta164]

@@bionicturtle For theta to be positive ,the following relationship should hold true i.e S(0)*N' (D1)*SIGMA/(2*sqrt(T0) < R*K*exp(-rt)*N(-d2). Is it possible mathematically?

[@scorpion55x]

It's "ceteris paribus" not "ceretus paribus". Great video!

[@易哲源]

For those who concerned about Positive Theta, Deep In-the-money options nowadays suffer from severe IV smile effects (e.g. IV = 50% for At-the-money, IV = 120% for Deep In-the-money) and thus Theta will never be Positive.

[@易哲源]

Go check Theta formula, the second term +rKeN(-d2) is not capable to compensate the first term if IV increased dramatically for Deep In-the-money options.