Actual put option values vs. Delta-estimated put option values

CFA Level II Derivatives
#1

Hi guys,

We know that the actual call line is significantly above the delta-estimated call line, implying that delta estimations underestimate the value of a call option.

I was wondering, does delta estimation also under-estimate the values of put options, or is the opposite true for actual put option values vs. delta-estimated put option values?

In other words, does delta-estimation lead to under or overstating a put option’s actual value?

Thanks and regards,

#2

I am going to assume that when you say “actual call line”, you are referring to call option value curve (which represents the call option value against the price of the underlying stock). The delta-estimated call value line is a tangent to this curve. Since the call option value curve is an upward-sloping convex curve, it thus follows (and you have correctly mentioned so) that the delta-estimated call value will underestimate the true value of the call option Going with the same logic, the put option value curve will be a downward- sloping convex curve (think about the bottom-left quadrant of a circle), and thus the delta-estimated put value , being a tangent to this curve, will also underestimate the true value of the put option.

Hope this helps!