I don’t understand why lower volatility, a shorter term, a lower risk free rate and a higher expected dividend yield would decrease the estimated fair value of the options and decrease compensation expense.

The lower the price volatility of the stock, the less likely that it will increase in value, reducing the time value of the option.

The shorter the term, the less time the stock has to increase in value, so the less likely that it will increase in value, reducing the time value of the option.

The lower the risk-free rate, the higher the present value of the exercise price, so the lower the intrinsic value (market price – PV(exercise price)) of the option.

The higher the expected dividend yield, the more value lost by owning the option (as compared to owning the stock: stock owners get the dividend; option owners do not).

But for the third part, when you say the intrinsic value of the option is market price -PV(exercise price), you are talking about the call option right?

For put option, PV (Exercise price) - market price, if the risk-free rate decreases, the PV (exercise price) would increase. As a result, the put option value would increase.