How are MtGox options going to affect Bitcoin price volatility? MtGox plans to introduce Options, would Bitcoin price become more stable or it would just hedge risks?
Probably both, though the effect may be pretty small.

Arguably, the most prudent use of options is reducing risk.  For example, a merchant with accounts receivable in Bitcoins would want to protect the value of the fixed amount of BTC he will receive.  Options can limit his downside risk.  At present the price volatility of Bitcoins hampers its use for commerce, since the value of an asking price in BTC varies so much from day to day.  With options to reduce risk, more businesses will be willing to accept Bitcoins, bringing more liquidity to the Bitcoin "ecosystem".  

Increased acceptance of Bitcoins and increased "money supply" are more likely than options to stabilize prices.  They would reduce price fluctuations caused by thin trading.  The same effect is seen in the stock market where relatively unknown stocks undergo drastic price swings due to somewhat small trades.  Conversely, a widely traded stock exhibits much less volatility.