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> We can see that a higher mean and a higher standard deviation result in higher option value. This is a pretty unconvincing argument, because increasing the s
by teraflop 6y ago
> We can see that a higher mean and a higher standard deviation result in higher option value.
This is a pretty unconvincing argument, because increasing the standard deviation increases the expected value of a lognormal distribution, even without any weird option payoffs being involved.
- smabie 6y agoIncreased volatility of the underlying always increases option prices. Moreover, a higher standard deviation decreases the compounded returns of a log normal distribution, not decreases it. This is called volatility drag, and is closesly related to the AM-GM inequality: the geometric and arithmetic means of a series are only equal if all terms are identical. If this is not true, an arithmetic average will always be greater.