maximum potential exposure from unexpected loss events that could be ceded to a reinsurer.
In addition, credit executives within ERM review reinsurer exposures and credit limits and approve reinsurer credit limits above specified levels.
Finally, even where we conclude that uncollateralized credit risk is acceptable, we require collateral from active reinsurance counterparties where it is necessary for our subsidiaries to recognize the reinsurance recoverable assets for statutory accounting purposes.
At December 31, 2016, we held $8.1 billion of collateral, in the form of funds withheld, securities in reinsurance trust accounts and/or evergreen letters of credit, in support of reinsurance recoverable assets from unaffiliated reinsurers.
We believe that no exposure to a single reinsurer represents an inappropriate concentration of risk to us.
The following table presents information for each reinsurer representing in excess of five percent of our total reinsurance recoverable assets:
## Table 0 ##
(a) The financial strength ratings reflect the ratings of the various reinsurance subsidiaries of the companies listed as of January 3, 2017.
(b) Total reinsurance assets include both the Property Casualty Insurance Companies and the Life Insurance Companies reinsurance recoverable.
(c) Excludes collateral held in excess of applicable balances.
(d) Includes $1.8 billion recoverable under the 2011 retroactive reinsurance transaction pursuant to which a large portion of the Property Casualty Insurance Companies net domestic asbestos liabilities were transferred to NICO.
Does not include reinsurance assets ceded to other reinsurers for which NICO has assumed the collection risk.
We entered into an adverse development reinsurance agreement with NICO, discussed in Item 7.
MD&A — Insurance Reserves — Reinsurance Activities.
Based on reserves as of December 31, 2016, this agreement will increase the gross reinsurance assets and collateral held from the Berkshire Hathaway Group of Companies by approximately $12.8 billion and $10.2 billion, respectively.
At December 31, 2016, we had no significant general reinsurance recoverable due from any individual reinsurer that was financially troubled.
Reinsurer capital levels remained stable in 2016, and the industry’s robust underwriting capacity resulted in continued competition and attractive rates for 2017 renewals.
Reduced profitability associated with lower rates could potentially result in reduced capacity or rating downgrades for some reinsurers.
The RCD, in conjunction with the credit executives within ERM, reviews these developments, monitors credit triggers that may require the reinsurer to post collateral, and seeks to use other appropriate means to mitigate any material risks arising from these developments.
See Item 7.
MD&A – Critical Accounting Estimates – Reinsurance Assets for further discussion of reinsurance recoverable.
Life Insurance Companies Key Insurance Risks Our Individual Retirement, Group Retirement, Life Insurance and Institutional Markets businesses manage risk through product design, experience monitoring, pricing actions, risk limitations, reinsurance and active monitoring and management of the relationships between assets and liabilities, including hedging.
For our Individual and Group Retirement and Life Insurance products offered by the Life Insurance Companies, key insurance risks include the following: ?
Mortality risk – represents the risk of loss arising from actual mortality rates being higher than expected mortality rates.
This risk could arise from pandemics or other events, including longer-term societal changes that cause higher than expected mortality.
This risk exists in a number of our product lines, but is most significant for our life insurance products.  ?
Longevity risk – represents the risk of a change in value of a policy or benefit as a result of actual mortality rates being lower than the expected mortality rates.
This risk could arise from longer-term societal health changes as well as other factors.
This risk exists in a number of our product lines but is most significant for our retirement, institutional and annuity products.  ?
Policyholder behavior risk including surrender/lapse risk – represents the risk that actual policyholder behavior differs from expected behavior in a manner that has an adverse effect on our results of operations.
There are many assumptions made when products are sold, including how long the contracts will persist.
Actual experience can vary significantly from these assumptions.
This risk is impacted by a number of factors including changes in market conditions, especially interest rate and equity market changes, tax law, regulations and policyholder preferences.
This risk exists in the majority of our product lines.  ?
Interest rate risk – represents the potential for loss due to a change in interest rates.
Interest rate risk is measured with respect to assets, liabilities (both insurance-related and financial) and derivatives.
This risk manifests itself when interest rates move significantly in a short period of time.
Rapidly rising interest rates create the potential for increased surrenders.
Interest rate risk
Group Retirement Group Retirement competes in the defined contribution market under its VALIC brand.
VALIC is a leading retirement plan provider in the U. S.  for K-12 schools and school districts, higher education, healthcare, government and other not-for-profit institutions.
The defined contribution market is a highly efficient and competitive market that requires support for both plan sponsors and individual participants.
To meet this challenge, VALIC is investing in a client-focused technology platform to support improved compliance and self-service functionality.
VALIC’s service model pairs self-service tools with its career financial advisors who provide individual plan participants with enrollment support and comprehensive financial planning services.
Changes in the interest rate environment have a significant impact on sales, surrender rates, investment returns, guaranteed income features, and spreads in the annuity industry.
See AIG’s Outlook –Industry and Economic Factors - Changes in the Interest Rate Environment for additional discussion of the impact of market interest rate movement on our Group Retirement business.
Group Retirement provides products and services to certain employee benefit plans that are subject to the requirements of the DOL Fiduciary Rule.
For additional information on the DOL Fiduciary Rule, including the recent decision by the new administration to request a further review of the DOL Fiduciary Rule, see Part I, Item 1.  Business – Regulation.
Life Insurance Consumers have increased needs for financial protection for beneficiaries, estate planning and wealth creation.
Life Insurance addresses the need for protection against the risk of premature death through a broad spectrum of products that include both term and permanent life insurance.
In addition, Life Insurance offers products and benefits that offset other risks such as chronic and critical illness.
In response to a sustained low interest rate environment, Life Insurance has been actively re-pricing products and shifting its focus away from products with long-duration interest rate guarantees by introducing new products with shorter guarantees as well as indexed universal life products.
See AIG’s Outlook –Industry and Economic Factors - Changes in the Interest Rate Environment for additional discussion of the impact of market interest rate movement on our Life Insurance business.
Personal Insurance The need for full life cycle products and coverage, increases in personal wealth accumulation, and awareness of insurance protection and risk management continue to support the growth of the Personal Insurance industry.
Personal Insurance focuses on group and corporate clients, together with individual customers within national markets.
We expect the demand for multinational cross-border coverage and services to increase due to the internationalization of clients and customers.
We believe our global presence provides Personal Insurance a distinct competitive advantage.
In Japan, the competition for auto insurance has intensified, in part driven by a decline in new car sales and the existence of fewer but larger insurers.
In addition, the overall market size in homeowners insurance contracted after the duration restriction on long-term fire insurance became effective in October 2015.
In the U. S. , we compete in the high net worth market and will continue to expand our innovative products and services to distribution partners and clients.
Outside of Japan and the U. S. , our Personal Insurance module continues to invest selectively in markets, which we believe have higher potential for sustainable profitability.
CONSUMER INSURANCE RESULTS
## Table 1 ##
The fair value for these options was estimated at the date of grant using a Black-Scholes option pricing model with the following weighted-average assumptions for 2006, 2005 and 2004:
## Table 2 ##
The Black-Scholes option valuation model was developed for use in estimating the fair value of traded options which have no vesting restrictions and are fully transferable.
In addition, option valuation models require the input of highly subjective assumptions, including the expected stock price volatility.
Because the Company’s employee stock options have characteristics significantly different from those of traded options, and because changes in the subjective input assumptions can materially affect the fair value estimate, in management’s opinion, the existing models do not necessarily provide a reliable single measure of the fair value of its employee stock options.
The total fair value of shares vested during 2006, 2005, and 2004 was $9,413, $8,249, and $6,418 respectively.
The aggregate intrinsic values of options outstanding and exercisable at December 30, 2006 were $204.1 million and $100.2 million, respectively.
The aggregate intrinsic value of options exercised during the year ended December 30, 2006 was $42.8 million.
Aggregate intrinsic value represents the positive difference between the Company’s closing stock price on the last trading day of the fiscal period, which was $55.66 on December 29, 2006, and the exercise price multiplied by the number of options outstanding.
As of December 30, 2006, there was $64.2 million of total unrecognized compensation cost related to unvested share-based compensation awards granted to employees under the option plans.
That cost is expected to be recognized over a period of five years.
Employee Stock Purchase Plan The shareholders also adopted an employee stock purchase plan (ESPP).
Up to 2,000,000 shares of common stock have been reserved for the ESPP.
Shares will be offered to employees at a price equal to the lesser of 85% of the fair market value of the stock on the date of purchase or 85% of the fair market value on the enrollment date.
The ESPP is intended to qualify as an “employee stock purchase plan” under Section 423 of the Internal Revenue Code.
During 2006, 2005, and 2004, 124,693, 112,798, and 117,900 shares were purchased under the plan for a total purchase price of $3,569, $2,824, and $2,691, respectively.
At December 30, 2006, approximately 1,116,811 shares were available for future issuance.

Tables referenced above, in order (Table 0 first):
<table><tr><td> At December 31, 2016</td><td></td><td rowspan="2">A.M. Best Rating<sup>(a)</sup></td><td rowspan="2">Gross Reinsurance Assets</td><td></td><td rowspan="2">Percent of Reinsurance Assets (b)</td><td></td><td rowspan="2">Uncollateralized Reinsurance Assets</td></tr><tr><td><i>(in millions)</i></td><td>S&P Rating<sup>(a)</sup></td><td></td><td>Collateral Held (c)</td></tr><tr><td> Reinsurer:</td><td> </td><td> </td><td></td><td> </td><td></td><td></td><td></td></tr><tr><td>Swiss Reinsurance Group of Companies</td><td> AA-</td><td> A+</td><td>$4,101</td><td> </td><td>18.7%</td><td>$1,480</td><td>$2,621</td></tr><tr><td>Berkshire Hathaway Group of Companies</td><td> AA+</td><td> A++</td><td>$2,165</td><td><sup>(d)</sup></td><td>9.9%</td><td>$1,595</td><td>$570</td></tr><tr><td>Munich Reinsurance Group of Companies</td><td> AA-</td><td> A+</td><td>$1,961</td><td> </td><td>9.0%</td><td>$734</td><td>$1,227</td></tr></table>
<table><tr><td> Years Ended December 31,</td><td></td><td></td><td></td><td colspan="2">Percentage Change</td></tr><tr><td><i>(in millions)</i></td><td>2016</td><td>2015</td><td>2014</td><td>2016 vs. 2015</td><td>2015 vs. 2014</td></tr><tr><td> Revenues:</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Premiums</td><td>$13,015</td><td>$12,620</td><td>$13,444</td><td>3%</td><td>-6%</td></tr><tr><td>Policy fees</td><td>2,411</td><td>2,450</td><td>2,347</td><td>-2</td><td>4</td></tr><tr><td>Net investment income</td><td>7,345</td><td>7,356</td><td>7,924</td><td>-</td><td>-7</td></tr><tr><td>Other income</td><td>1,278</td><td>2,104</td><td>1,998</td><td>-39</td><td>5</td></tr><tr><td>Total operating revenue</td><td>24,049</td><td>24,530</td><td>25,713</td><td>-2</td><td>-5</td></tr><tr><td> Benefits and expenses:</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Policyholder benefits and losses incurred</td><td>8,858</td><td>8,760</td><td>8,809</td><td>1</td><td>-1</td></tr><tr><td>Interest credited to policyholder account balances</td><td>3,205</td><td>3,207</td><td>3,246</td><td>-</td><td>-1</td></tr><tr><td>Amortization of deferred policy acquisition costs</td><td>2,681</td><td>2,762</td><td>2,655</td><td>-3</td><td>4</td></tr><tr><td>General operating and other expenses<sup>*</sup></td><td>5,456</td><td>6,872</td><td>6,797</td><td>-21</td><td>1</td></tr><tr><td>Total operating expenses</td><td>20,200</td><td>21,601</td><td>21,507</td><td>-6</td><td>-</td></tr><tr><td> Pre-tax operating income</td><td>$3,849</td><td>$2,929</td><td>$4,206</td><td>31%</td><td>-30%</td></tr></table>
<table><tr><td></td><td>2006</td><td>2005</td><td>2004</td></tr><tr><td>Weighted average fair value of options granted</td><td>$20.01</td><td>$9.48</td><td>$7.28</td></tr><tr><td>Expected volatility</td><td>0.3534</td><td>0.3224</td><td>0.3577</td></tr><tr><td>Distribution yield</td><td>1.00%</td><td>0.98%</td><td>1.30%</td></tr><tr><td>Expected life of options in years</td><td>6.3</td><td>6.3</td><td>6.3</td></tr><tr><td>Risk-free interest rate</td><td>5%</td><td>4%</td><td>4%</td></tr></table>

Question: considering the weighted average fair value of options , how many shares vested in 2004?
Answer: 881.593
Reasoning program: divide(6418,7.28)